@article{chattopadhyay_ott_schafer_skokov_2023, title={Dynamic scaling of order parameter fluctuations in model B}, volume={108}, ISSN={["2470-0029"]}, url={https://doi.org/10.1103/PhysRevD.108.074004}, DOI={10.1103/PhysRevD.108.074004}, abstractNote={We describe numerical simulations of the stochastic diffusion equation with a conserved charge. We focus on the dynamics in the vicinity of a critical point in the Ising universality class. The model we consider is expected to describe the critical dynamics near a possible QCD critical point if the coupling of the order parameter to the momentum density of the fluid can be neglected. The simulations are performed on a spatial lattice, and the time evolution is performed using a Metropolis algorithm. We determine the dynamical critical exponent $z\simeq 3.972(2)$, which agrees with predictions of the epsilon expansion. We also study non-equilibrium sweeps of the reduced temperature and observe approximate Kibble-Zurek scaling.}, number={7}, journal={PHYSICAL REVIEW D}, author={Chattopadhyay, Chandrodoy and Ott, Josh and Schafer, Thomas and Skokov, Vladimir}, year={2023}, month={Oct} }
 @article{chattopadhyay_heinz_schaefer_2023, title={Far-off-equilibrium expansion trajectories in the QCD phase diagram}, volume={107}, ISSN={["2469-9993"]}, url={https://doi.org/10.1103/PhysRevC.107.044905}, DOI={10.1103/PhysRevC.107.044905}, abstractNote={We consider the hydrodynamic evolution of a quark-gluon gas with non-zero quark masses and net baryon number in its phase diagram. For far-off-equilibrium initial conditions the expansion trajectories appear to violate simple rules based on the second law of thermodynamics that were previously established for ideal or weakly dissipative fluids. For Bjorken flow we present a detailed analysis within kinetic theory that provides a full microscopic understanding of these macroscopic phenomena and establishes their thermodynamic consistency. We point out that, for certain far-off-equilibrium initial conditions, the well-known phenomenon of"viscous heating"turns into"viscous cooling"where, driven by dissipative effects, the temperature decreases faster than in adiabatic expansion.}, number={4}, journal={PHYSICAL REVIEW C}, author={Chattopadhyay, Chandrodoy and Heinz, Ulrich and Schaefer, Thomas}, year={2023}, month={Apr} }
 @article{chattopadhyay_heinz_schäfer_2023, title={Fluid dynamics from the Boltzmann equation using a maximum entropy distribution}, volume={108}, url={https://doi.org/10.1103/PhysRevC.108.034907}, DOI={10.1103/PhysRevC.108.034907}, abstractNote={Using the recently developed ``Maximum Entropy'' (or ``least biased'') distribution function to truncate the moment hierarchy arising from kinetic theory, we formulate a far-from-equilibrium macroscopic theory that provides the possibility of describing both free-streaming and hydrodynamic regimes of heavy-ion collisions within a single framework. Unlike traditional hydrodynamic theories that include viscous corrections to finite order, the present formulation incorporates contributions to all orders in shear and bulk inverse Reynolds numbers, allowing it to handle large dissipative fluxes. By considering flow profiles relevant for heavy-ion collisions (Bjorken and Gubser flows), we demonstrate that the present approach provides excellent agreement with underlying kinetic theory throughout the fluid's evolution and, especially, in far-off-equilibrium regimes where traditional hydrodynamics breaks down.}, number={3}, journal={Physical Review C}, author={Chattopadhyay, Chandrodoy and Heinz, Ulrich and Schäfer, Thomas}, year={2023}, month={Sep}, pages={034907} }
 @article{chao_schafer_2023, title={N-particle irreducible actions for stochastic fluids}, volume={06}, ISSN={["1029-8479"]}, url={https://doi.org/10.1007/JHEP06(2023)057}, DOI={10.1007/JHEP06(2023)057}, abstractNote={We construct one- and two-particle irreducible (1PI and 2PI) effective actions for the stochastic fluid dynamics of a conserved density undergoing diffusive motion. We compute the 1PI action at one-loop order, and the 2PI action in two-loop approximation. We derive a set of Schwinger-Dyson equations, and regularize the resulting equations using Pauli-Villars fields. We numerically solve the Schwinger-Dyson equations for a non-critical fluid. We find that higher-loop effects summed by the Schwinger-Dyson renormalize the non-linear coupling. We also find indications of a diffuson-cascade, the appearance $n$-loop corrections with smaller and smaller exponential suppression.}, number={6}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Chao, Jingyi and Schafer, Thomas}, year={2023}, month={Jun} }
 @article{schafer_skokov_2022, title={Dynamics of non-Gaussian fluctuations in model A}, volume={106}, ISSN={["2470-0029"]}, url={https://doi.org/10.1103/PhysRevD.106.014006}, DOI={10.1103/PhysRevD.106.014006}, abstractNote={Motivated by the experimental search for the QCD critical point we perform simulations of a stochastic field theory with purely relaxational dynamics (model A). We verify the expected dynamic scaling of correlation functions. Using a finite size scaling analysis we obtain the dynamic critical exponent $z=2.026(56)$. We investigate time dependent correlation functions of higher moments $M^n(t)$ of the order parameter $M(t)$ for $n=1,2,3,4$. We obtain dynamic scaling with the same critical exponent $z$ for all $n$, but the relaxation constant depends on $n$. We also study the relaxation of $M^n(t)$ after a quench, where the simulation is initialized in the high temperature phase, and the dynamics is studied at the critical temperature $T_c$. We find that the evolution does not follow simple scaling with the dynamic exponent $z$, and that it involves an early time rise followed by late stage relaxation.}, number={1}, journal={PHYSICAL REVIEW D}, author={Schafer, Thomas and Skokov, Vladimir}, year={2022}, month={Jul} }
 @article{hou_schafer_2021, title={Dissipative superfluid hydrodynamics for the unitary Fermi gas}, volume={104}, ISSN={["2469-9934"]}, url={http://inspirehep.net/record/1863038}, DOI={10.1103/PhysRevA.104.023313}, abstractNote={In this work we establish constraints on the temperature dependence of the shear viscosity $\eta$ in the superfluid phase of a dilute Fermi gas in the unitary limit. Our results are based on analyzing experiments that measure the aspect ratio of a deformed cloud after release from an optical trap. We discuss how to apply the two-fluid formalism to the unitary gas, and provide a suitable parametrization of the equation of state. We show that in expansion experiments the difference between the normal and superfluid velocities remains small, and can be treated as a perturbation. We find that expansion experiments favor a shear viscosity that decreases significantly in the superfluid regime. Using an exponential parametrization we find $\eta(T_c/(2T_F))<0.37\eta (T_c/T_F)$, where $T_c$ is the critical temperature, $T_F$ is the local Fermi temperature of the gas.}, number={2}, journal={PHYSICAL REVIEW A}, author={Hou, Jiaxun and Schafer, Thomas}, year={2021}, month={Aug} }
 @article{chao_schafer_2021, title={Multiplicative noise and the diffusion of conserved densities}, volume={01}, ISSN={["1029-8479"]}, url={http://inspirehep.net/record/1810034}, DOI={10.1007/JHEP01(2021)071}, abstractNote={Abstract}, number={1}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Chao, Jingyi and Schafer, Thomas}, year={2021}, month={Jan} }
 @article{behtash_kamata_martinez_schafer_skokov_2021, title={Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons}, volume={103}, ISSN={["2470-0029"]}, url={http://inspirehep.net/record/1830583}, DOI={10.1103/PhysRevD.103.056010}, abstractNote={We investigate the non-linear transport processes and hydrodynamization of a system of gluons undergoing longitudinal boost-invariant expansion. The dynamics is described within the framework of the Boltzmann equation in the small-angle approximation. The kinetic equations for a suitable set of moments of the one-particle distribution function are derived. By investigating the stability and asymptotic resurgent properties of this dynamical system, we demonstrate, that its solutions exhibit a rather different behavior for large (UV) and small (IR) effective Knudsen numbers. Close to the forward attractor in the IR regime the constitutive relations of each moment can be written as a multiparameter transseries. This resummation scheme allows us to extend the definition of a transport coefficient to the non-equilibrium regime naturally. Each transport coefficient is renormalized by the non-perturbative contributions of the non-hydrodynamic modes. The Knudsen number dependence of the transport coefficient is governed by the corresponding renormalization group flow equation. An interesting feature of the Yang-Mills plasma in this regime is that it exhibits transient non-Newtonian behavior while hydrodynamizing. In the UV regime the solution for the moments can be written as a power-law asymptotic series with a finite radius of convergence. We show that radius of convergence of the UV perturbative expansion grows linearly as a function of the shear viscosity to entropy density ratio. Finally, we compare the universal properties in the pullback and forward attracting regions to other kinetic models including the relaxation time approximation and the effective kinetic Arnold-Moore-Yaffe (AMY) theory.}, number={5}, journal={PHYSICAL REVIEW D}, publisher={American Physical Society (APS)}, author={Behtash, A. and Kamata, S. and Martinez, M. and Schafer, T. and Skokov, V}, year={2021}, month={Mar} }
 @article{bluhm_kalweit_nahrgang_arslandok_braun-munzinger_floerchinger_fraga_gazdzicki_hartnack_herold_et al._2020, title={Dynamics of critical fluctuations: Theory – phenomenology – heavy-ion collisions}, volume={1003}, url={http://inspirehep.net/record/1777146}, DOI={10.1016/j.nuclphysa.2020.122016}, abstractNote={This report summarizes the presentations and discussions during the Rapid Reaction Task Force “Dynamics of critical fluctuations: Theory – phenomenology – heavy-ion collisions”, which was organized by the ExtreMe Matter Institute EMMI and held at GSI, Darmstadt, Germany in April 2019. We address the current understanding of the dynamics of critical fluctuations in QCD and their measurement in heavy-ion collision experiments. In addition, we outline what might be learned from studying correlations in other physical systems, such as cold atomic gases.}, journal={Nucl.Phys.A}, author={Bluhm, Marcus and Kalweit, Alexander and Nahrgang, Marlene and Arslandok, Mesut and Braun-Munzinger, Peter and Floerchinger, Stefan and Fraga, Eduardo S. and Gazdzicki, Marek and Hartnack, Christoph and Herold, Christoph and et al.}, year={2020}, month={Nov}, pages={122016} }
 @article{cherman_kamata_schäfer_ünsal_2020, title={Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories}, volume={101}, url={http://inspirehep.net/record/1761483}, DOI={10.1103/PhysRevD.101.014012}, abstractNote={We investigate the singularity structure of the $(-1)^F$ graded partition function in QCD with $n_f \geq 1$ massive adjoint fermions in the large-$N$ limit. Here, $F$ is fermion number and $N$ is the number of colors. The large $N$ partition function is made reliably calculable by taking space to be a small three-sphere $S^3$. Singularites in the graded partition function are related to phase transitions and to Hagedorn behavior in the $(-1)^F$-graded density of states. We study the flow of the singularities in the complex "inverse temperature" $\beta$ plane as a function of the quark mass. This analysis is a generalization of the Lee-Yang-Fisher-type analysis for a theory which is always in the thermodynamic limit thanks to the large $N$ limit. We identify two distinct mechanisms for the appearance of physical Hagedorn singularities and center-symmetry changing phase transitions at real positive $\beta$, inflow of singularities from the $\beta=0$ point, and collisions of complex conjugate pairs of singularities.}, number={1}, journal={Phys.Rev.D}, publisher={American Physical Society (APS)}, author={Cherman, Aleksey and Kamata, Syo and Schäfer, Thomas and Ünsal, Mithat}, year={2020}, month={Jan}, pages={014012} }
 @article{parotto_bluhm_mroczek_nahrgang_noronha-hostler_rajagopal_ratti_schafer_stephanov_2020, title={QCD equation of state matched to lattice data and exhibiting a critical point singularity}, volume={101}, ISSN={["2469-9993"]}, url={http://inspirehep.net/record/1672952}, DOI={10.1103/PhysRevC.101.034901}, abstractNote={We construct a family of equations of state for QCD in the temperature range 30MeV≤T≤800MeV and in the chemical potential range 0≤μB≤450MeV. These equations of state match available lattice QCD results up to O(μB4) and in each of them we place a critical point in the three-dimensional (3D) Ising model universality class. The position of this critical point can be chosen in the range of chemical potentials covered by the second Beam Energy Scan at the Relativistic Heavy Ion Collider. We discuss possible choices for the free parameters, which arise from mapping the Ising model onto QCD. Our results for the pressure, entropy density, baryon density, energy density, and speed of sound can be used as inputs in the hydrodynamical simulations of the fireball created in heavy ion collisions. We also show our result for the second cumulant of the baryon number in thermal equilibrium, displaying its divergence at the critical point. In the future, comparisons between RHIC data and the output of the hydrodynamic simulations, including calculations of fluctuation observables, built upon the model equations of state that we have constructed may be used to locate the critical point in the QCD phase diagram, if there is one to be found.}, number={3}, journal={PHYSICAL REVIEW C}, author={Parotto, Paolo and Bluhm, Marcus and Mroczek, Debora and Nahrgang, Marlene and Noronha-Hostler, J. and Rajagopal, Krishna and Ratti, Claudia and Schafer, Thomas and Stephanov, Mikhail}, year={2020}, month={Mar} }
 @article{schaefer_2020, title={Quantum limited sound attenuation in a dilute atomic Fermi gas}, volume={12}, url={http://inspirehep.net/record/1838260}, DOI={10.1126/science.abb6155}, abstractNote={Resonantly interacting atoms confined by lasers have implications for neutron stars}, author={Schaefer, Thomas}, year={2020}, month={Dec} }
 @article{martinez_schäfer_skokov_2019, title={Critical behavior of the bulk viscosity in QCD}, volume={100}, url={http://inspirehep.net/record/1741788}, DOI={10.1103/PhysRevD.100.074017}, abstractNote={We study the behavior of the bulk viscosity $\zeta$ in QCD near a possible critical endpoint in the phase diagram. We verify the expectation that $(\zeta/s)\sim a(\xi/\xi_0)^{x_\zeta}$, where $s$ is the entropy density, $\xi$ is the correlation length, $\xi_0$ is the non-critical correlation length, $a$ is a constant and $x_\zeta\simeq 3$. Using a recently developed equation of state that includes a critical point in the universality class of the Ising model we estimate the constant of proportionality $a$. We find that $a$ is typically quite small, $a\sim O(10^{-4})$. We observe, however, that the result is sensitive to the commonly made assumption that the Ising temperature axis is approximately aligned with the QCD baryon chemical potential axis. If this is not the case, then the critical $\zeta/s$ can approach the non-critical value of $\eta/s$, where $\eta$ is the shear viscosity, even if the enhancement of the correlation length is modest, $\xi/\xi_0\sim 2$.}, number={7}, journal={Phys.Rev.D}, publisher={American Physical Society (APS)}, author={Martinez, M. and Schäfer, T. and Skokov, V.}, year={2019}, month={Oct}, pages={074017} }
 @article{nahrgang_bluhm_schafer_bass_2019, title={Diffusive dynamics of critical fluctuations near the QCD critical point}, volume={99}, ISSN={["1550-2368"]}, url={http://inspirehep.net/record/1667859}, DOI={10.1103/PhysRevD.99.116015}, abstractNote={A quantitatively reliable theoretical description of the dynamics of fluctuations in nonequilibrium is indispensable in the experimental search for the QCD critical point by means of ultrarelativistic heavy-ion collisions. In this paper we consider the fluctuations of the net-baryon density which becomes the slow, critical mode near the critical point. Due to net-baryon number conservation the dynamics is described by the fluid dynamical diffusion equation, which we extend to contain a white noise stochastic current. Including nonlinear couplings from the 3d Ising model universality class in the free energy functional, we solve the fully interacting theory in a finite size system. We observe that purely Gaussian white noise generates non-Gaussian fluctuations, but finite size effects and exact net-baryon number conservation lead to significant deviations from the expected behavior in equilibrated systems. In particular the skewness shows a qualitative deviation from infinite volume expectations. With this benchmark established we study the real-time dynamics of the fluctuations. We recover the expected dynamical scaling behavior and observe retardation effects and the impact of critical slowing down near the pseudocritical temperature.}, number={11}, journal={PHYSICAL REVIEW D}, author={Nahrgang, Marlene and Bluhm, Marcus and Schafer, Thomas and Bass, Steffen A.}, year={2019}, month={Jun} }
 @article{martinez_schafer_2019, title={Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid}, volume={99}, ISSN={["2469-9993"]}, url={http://inspirehep.net/record/1708859}, DOI={10.1103/PhysRevC.99.054902}, abstractNote={We investigate the impact of hydrodynamic fluctuations on correlation functions in a scale invariant fluid with a conserved $U(1)$ charge. The kinetic equations for the two-point functions of pressure, momentum and heat energy densities are derived within the framework of stochastic hydrodynamics. The leading non-analytic contributions to the energy-momentum tensor as well as the $U(1)$ current are determined from the solutions to these kinetic equations. In the case of a static homogeneous background we show that the long time tails obtained from hydro-kinetic equations reproduce the one-loop results derived from statistical field theory. We use these results to establish bounds on transport coefficients. We generalize the stochastic equation to a background flow undergoing Bjorken expansion. We compute the leading fractional power $\mathcal{O}((\tau T)^{-3/2})$ correction to the $U(1)$ current and compare with the first order gradient term.}, number={5}, journal={PHYSICAL REVIEW C}, author={Martinez, M. and Schafer, T.}, year={2019}, month={May} }
 @article{behtash_dunne_schafer_sulejmanpasic_unsal_2018, title={Critical points at infinity, non-Gaussian saddles, and bions}, volume={06}, ISSN={["1029-8479"]}, url={http://inspirehep.net/record/1665487}, DOI={10.1007/jhep06(2018)068}, abstractNote={Abstract
          }, number={6}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Behtash, Alireza and Dunne, Gerald V and Schafer, Thomas and Sulejmanpasic, Tin and Unsal, Mithat}, year={2018}, month={Jun} }
 @article{bluhm_nahrgang_schaefer_bass_2018, title={Fluctuating fluid dynamics for the QGP in the LHC and BES era}, volume={171}, ISSN={["2100-014X"]}, url={http://inspirehep.net/record/1667033}, DOI={10.1051/epjconf/201817116004}, abstractNote={In an era of high-precision determinations of QGP properties a full incorporation of fluid dynamical fluctuations into our models has become crucial, in particular, when describing the dynamics of small systems or near the conjectured QCD critical point. In this talk we discuss some effects of the propagation of these fluctuations. For LHC physics we focus on fluctuations in the energy-momentum tensor, while the impact of fluctuations in the diffusive net-baryon density is studied to improve our knowledge on the formation of critical fluctuations being searched in current and future BES programs.}, journal={17TH INTERNATIONAL CONFERENCE ON STRANGENESS IN QUARK MATTER (SQM 2017)}, author={Bluhm, Marcus and Nahrgang, Marlene and Schaefer, Thomas and Bass, Steffen A.}, year={2018} }
 @inproceedings{nahrgang_bluhm_schäfer_bass_2017, title={Baryon number diffusion with critical fluctuations}, volume={967}, url={http://inspirehep.net/record/1628341}, DOI={10.1016/j.nuclphysa.2017.04.021}, abstractNote={The description of dynamical fluctuations near the QCD critical point in heavy-ion collisions is crucial for understanding the existing and upcoming experimental data from the beam energy scan programs. In this talk we discuss the evolution of fluctuations of the net-baryon density as given by a stochastic diffusion equation. We study equilibrium as well as dynamical systems for which we can show the impact of nonequilibrium effects on the second-order moment.}, booktitle={Nucl.Phys.A}, author={Nahrgang, Marlene and Bluhm, Marcus and Schäfer, Thomas and Bass, Steffen A.}, year={2017}, month={Nov}, pages={824–827} }
 @article{bluhm_nahrgang_bass_schafer_2017, place={Berkeley, United States}, title={Behavior of universal critical parameters in the QCD phase diagram}, volume={779}, ISSN={["1742-6596"]}, url={http://inspirehep.net/record/1503418}, DOI={10.1088/1742-6596/779/1/012074}, abstractNote={We determine the dependence of important parameters for critical fluctuations on temperature and baryon chemical potential in the QCD phase diagram. The analysis is based on an identification of the fluctuations of the order parameter obtained from the Ising model equation of state and the Ginzburg-Landau effective potential approach. The impact of the mapping from Ising model variables to QCD thermodynamics is discussed.}, number={1}, journal={16TH INTERNATIONAL CONFERENCE ON STRANGENESS IN QUARK MATTER (SQM2016)}, author={Bluhm, Marcus and Nahrgang, Marlene and Bass, Steffen A. and Schafer, Thomas}, year={2017} }
 @article{bluhm_hou_schafer_2017, title={Determination of the Density and Temperature Dependence of the Shear Viscosity of a Unitary Fermi Gas Based on Hydrodynamic Flow}, volume={119}, ISSN={["1079-7114"]}, url={http://inspirehep.net/record/1591363}, DOI={10.1103/PhysRevLett.119.065302}, abstractNote={We determine the shear viscosity of the ultracold Fermi gas at unitarity in the normal phase using hydrodynamic expansion data. The analysis is based on a generalized fluid dynamic framework which ensures a smooth transition between the fluid dynamic core of the cloud and the ballistic corona. We use expansion data taken by Joseph, Elliott, and Thomas [Shear Viscosity of a Universal Fermi Gas Near the Superfluid Phase Transition, Phys. Rev. Lett. 115, 020401 (2015).PRLTAO0031-900710.1103/PhysRevLett.115.020401] and measurements of the equation of state by Ku et al. [Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas, Science 335, 563 (2012).SCIEAS0036-807510.1126/science.1214987]. We find that the shear viscosity to particle density ratio just above the critical temperature is η/n|_{T_{c}}=0.41±0.11. We also obtain evidence that the shear viscosity to entropy density ratio has a minimum slightly above T_{c} with η/s|_{min}=0.50±0.10.}, number={6}, journal={PHYSICAL REVIEW LETTERS}, author={Bluhm, Marcus and Hou, Jiaxun and Schafer, Thomas}, year={2017}, month={Aug} }
 @inproceedings{bluhm_schäfer_2017, title={From cold Fermi fluids to the hot QGP}, volume={10}, url={http://inspirehep.net/record/1601162}, DOI={10.5506/APhysPolBSupp.10.481}, abstractNote={Strongly coupled quantum fluids are found in different forms, including ultracold Fermi gases or tiny droplets of extremely hot Quark-Gluon Plasma. Although the systems differ in temperature by many orders of magnitude, they exhibit a similar almost inviscid fluid dynamical behavior. In this work, we summarize some of the recent theoretical developments toward better understanding this property in cold Fermi gases at and near unitarity.}, booktitle={Acta Phys.Polon.Supp.}, author={Bluhm, Marcus and Schäfer, Thomas}, year={2017}, month={May}, pages={481} }
 @article{martinez_schäfer_2017, title={Hydrodynamic tails and a fluctuation bound on the bulk viscosity}, volume={96}, url={http://inspirehep.net/record/1614503}, DOI={10.1103/PhysRevA.96.063607}, abstractNote={We study the small frequency behavior of the bulk viscosity spectral function using stochastic fluid dynamics. We obtain a number of model independent results, including the long-time tail of the bulk stress correlation function, and the leading non-analyticity of the spectral function at small frequency. We also establish a lower bound on the bulk viscosity which is weakly dependent on assumptions regarding the range of applicability of fluid dynamics. The bound on the bulk viscosity $\zeta$ scales as $\zeta_{\it min} \sim (P-\frac{2}{3}{\cal E})^2 \sum_i D_i^{-2}$, where $D_i$ are the diffusion constants for energy and momentum, and $P-\frac{2}{3}{\cal E}$, where $P$ is the pressure and ${\cal E}$ is the energy density, is a measure of scale breaking. Applied to the cold Fermi gas near unitarity, $|\lambda/a_s|\geq 1$ where $\lambda$ is the thermal de Broglie wave length and $a_s$ is the $s$-wave scattering length, this bound implies that the ratio of bulk viscosity to entropy density satisfies $\zeta/s \geq 0.1\hbar/k_B$. Here, $\hbar$ is Planck's constant and $k_B$ is Boltzmann's constant.}, number={6}, journal={Phys.Rev.A}, author={Martinez, Mauricio and Schäfer, Thomas}, year={2017}, month={Dec}, pages={063607} }
 @article{bluhm_nahrgang_bass_schafer_2017, title={Impact of resonance decays on critical point signals in net-proton fluctuations}, volume={77}, ISSN={["1434-6052"]}, url={http://inspirehep.net/record/1502951}, DOI={10.1140/epjc/s10052-017-4771-3}, abstractNote={The non-monotonic beam energy dependence of the higher cumulants of net-proton fluctuations is a widely studied signature of the conjectured presence of a critical point in the QCD phase diagram. In this work we study the effect of resonance decays on critical fluctuations. We show that resonance effects reduce the signatures of critical fluctuations, but that for reasonable parameter choices critical effects in the net-proton cumulants survive. The relative role of resonance decays has a weak dependence on the order of the cumulants studied with a slightly stronger suppression of critical effects for higher-order cumulants.}, number={4}, journal={EUROPEAN PHYSICAL JOURNAL C}, author={Bluhm, Marcus and Nahrgang, Marlene and Bass, Steffen A. and Schafer, Thomas}, year={2017}, month={Apr} }
 @inbook{schäfer_2017, title={Quantum Chromodynamics}, volume={936}, url={http://inspirehep.net/record/1599300}, DOI={10.1007/978-3-319-53336-0_2}, abstractNote={We present a brief introduction to QCD, the QCD phase diagram, and non-equilibrium phenomena in QCD. We emphasize aspects of the theory that can be addressed using computational methods, in particular euclidean path integral Monte Carlo, fluid dynamics, kinetic theory, classical field theory and holographic duality.}, booktitle={Lect.Notes Phys.}, author={Schäfer, Thomas}, year={2017}, pages={5–54} }
 @inproceedings{diamantini_kharzeev_molochkov_schäfer_sulejmanpašić_2017, place={Thessaloniki, Greece}, title={Round table: What can we learn about confinement and anoma-lous effects in QCD using analog systems?}, volume={137}, url={http://inspirehep.net/record/1504972}, DOI={10.1051/epjconf/201713701002}, abstractNote={We discuss an number of examples for recent connections between emergent phenomena in many-body systems in atomic and condensed matter physics, and confinement and other non-perturbative phenomena in quantum chromodynamics.}, booktitle={EPJ Web Conf.}, author={Diamantini, M. Cristina and Kharzeev, Dmitri E. and Molochkov, Alexander and Schäfer, Thomas and Sulejmanpašić, Tin}, year={2017}, month={Dec}, pages={01002} }
 @article{behtash_dunne_schaefer_sulejmanpasic_uensal_2017, title={Toward Picard-Lefschetz theory of path integrals, complex saddles and resurgence}, volume={2}, ISSN={["2380-2898"]}, url={http://inspirehep.net/record/1397667}, DOI={10.4310/amsa.2017.v2.n1.a3}, abstractNote={We show that the semi-classical analysis of generic Euclidean path integrals necessarily requires complexification of the action and measure, and consideration of complex saddle solutions.We demonstrate that complex saddle points have a natural interpretation in terms of the Picard–Lefschetz theory. Motivated in part by the semi-classical expansion of QCD with adjoint matter on $\mathbb{R}^3 \times S^1$, we study quantum-mechanical systems with bosonic and fermionic (Grassmann) degrees of freedom with harmonic degenerate minima, as well as (related) purely bosonic systems with harmonic nondegenerate minima. We find exact finite action non-BPS bounce and bion solutions to the holomorphic Newton equations. We find not only real solutions, but also complex solution with non-trivial monodromy, and finally complex multi-valued and singular solutions. Complex bions are necessary for obtaining the correct nonperturbative structure of these models. In the supersymmetric limit the complex solutions govern the ground state properties, and their contribution to the semiclassical expansion is necessary to obtain consistency with the supersymmetry algebra. The multi-valuedness of the action is either related to the hidden topological angle or to the resurgent cancellation of ambiguities. We also show that in the approximate multi-instanton description the integration over the complex quasi-zero mode thimble produces the most salient features of the exact solutions. While exact complex saddles are more difficult to construct in quantum field theory, the relation to the approximate thimble construction suggests that such solutions may be underlying some remarkable features of approximate bion saddles in quantum field theories.}, number={1}, journal={ANNALS OF MATHEMATICAL SCIENCES AND APPLICATIONS}, author={Behtash, Alireza and Dunne, Gerald V. and Schaefer, Thomas and Sulejmanpasic, Tin and Uensal, Mithat}, year={2017}, pages={95–212} }
 @inproceedings{nahrgang_bluhm_schäfer_bass_2017, title={Toward the description of fluid dynamical fluctuations in heavy-ion collisions}, volume={10}, url={http://inspirehep.net/record/1591362}, DOI={10.5506/APhysPolBSupp.10.687}, abstractNote={In this talk we present results obtained when fluid dynamical fluctuations are included in relativistic $3+1$ dimensional viscous fluid dynamics. We discuss effects of the interactions of fluctuations due to nonlinearities and the cutoff dependence.}, booktitle={Acta Phys.Polon.Supp.}, author={Nahrgang, Marlene and Bluhm, Marcus and Schäfer, Thomas and Bass, Steffen}, year={2017}, pages={687} }
 @article{cherman_schafer_unsal_2016, title={Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD}, volume={117}, ISSN={["1079-7114"]}, url={http://inspirehep.net/record/1449992}, DOI={10.1103/PhysRevLett.117.081601}, abstractNote={We show that there exists a special compactification of QCD on R^{3}×S^{1} in which the theory has a domain where continuous chiral symmetry breaking is analytically calculable. We give a microscopic derivation of the chiral Lagrangian, the chiral condensate, and the Gell-Mann-Oakes-Renner relation m_{π}^{2}f_{π}^{2}=-m_{q}⟨q[over ¯]q⟩. Abelian duality, monopole operators, and flavor-twisted boundary conditions play the main roles. The flavor twisting leads to the new effect of fractional jumping of fermion zero modes among monopole instantons. Chiral symmetry breaking is induced by monopole-instanton operators, and the Nambu-Goldstone pions arise by color-flavor transmutation from gapless "dual photons." We also give a microscopic picture of the "constituent quark" masses. Our results are consistent with expectations from chiral perturbation theory at large S^{1}, and yield strong support for adiabatic continuity between the small-S^{1} and large-S^{1} regimes. We also find concrete microscopic connections between N=1 and N=2 supersymmetric gauge theory dynamics and nonsupersymmetric QCD dynamics.}, number={8}, journal={PHYSICAL REVIEW LETTERS}, author={Cherman, Aleksey and Schafer, Thomas and Unsal, Mithat}, year={2016}, month={Aug} }
 @article{behtash_dunne_schaefer_sulejmanpasic_uensal_2016, title={Complexified Path Integrals, Exact Saddles, and Supersymmetry}, volume={116}, ISSN={["1079-7114"]}, url={http://inspirehep.net/record/1396147}, DOI={10.1103/physrevlett.116.011601}, abstractNote={In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semiclassical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex saddle points, even when the parameters in the action are real. We find new exact complex saddles, and show that without their contribution the semiclassical expansion is in conflict with basic properties such as the positive semidefiniteness of the spectrum, as well as constraints of supersymmetry. Generic saddles are not only complex, but also possibly multivalued and even singular. This is in contrast to instanton solutions, which are real, smooth, and single valued. The multivaluedness of the action can be interpreted as a hidden topological angle, quantized in units of π in supersymmetric theories. The general ideas also apply to nonsupersymmetric theories.}, number={1}, journal={PHYSICAL REVIEW LETTERS}, author={Behtash, Alireza and Dunne, Gerald V. and Schaefer, Thomas and Sulejmanpasic, Tin and Uensal, Mithat}, year={2016}, month={Jan} }
 @article{schäfer_2016, title={Generalized theory of diffusion based on kinetic theory}, volume={94}, url={http://inspirehep.net/record/1482387}, DOI={10.1103/PhysRevA.94.043644}, abstractNote={We propose to use spin hydrodynamics, a two-uid model of spin propagation, as a generalization of the diusion equation. We show that in the dense limit spin hydrodynamics reduces to Fick’s law and the diusion equation. In the opposite limit spin hydrodynamics is equivalent to a collisionless Boltzmann treatment of spin propagation. Spin hydrodynamics avoids unphysical eects that arise when the diusion equation is used to describe to a strongly interacting gas with a dilute corona. We apply spin hydrodynamics to the problem of spin diusion in a trapped atomic gas. We nd that the observed spin relaxation rate in the high temperature limit [Sommer et al., Nature 472, 201 (2011)] is consistent with the diusion constant predicted by kinetic theory.}, number={4}, journal={Phys.Rev.A}, author={Schäfer, T.}, year={2016}, month={Oct}, pages={043644} }
 @article{bluhm_schaefer_2016, title={Model-Independent Determination of the Shear Viscosity of a Trapped Unitary Fermi gas: Application to High-Temperature Data}, volume={116}, ISSN={["1079-7114"]}, url={http://inspirehep.net/record/1407992}, DOI={10.1103/physrevlett.116.115301}, abstractNote={Determinations of the shear viscosity of trapped ultracold gases suffer from systematic, uncontrolled uncertainties related to the treatment of the dilute part of the gas cloud. In this work we present an analysis of expansion experiments based on a new method, anisotropic fluid dynamics, that interpolates between Navier-Stokes fluid dynamics at the center of the cloud and ballistic behavior in the dilute corona. We validate the method using a comparison between anisotropic fluid dynamics and numerical solutions of the Boltzmann equation. We then apply anisotropic fluid dynamics to the expansion data reported by Cao et al. In the high-temperature limit we find η=0.282(mT)^{3/2}, which agrees within about 5% with the theoretical prediction η=0.269(mT)^{3/2}.}, number={11}, journal={PHYSICAL REVIEW LETTERS}, author={Bluhm, M. and Schaefer, T.}, year={2016}, month={Mar} }
 @misc{braun-munzinger_koch_schaefer_stachel_2016, title={Properties of hot and dense matter from relativistic heavy ion collisions}, volume={621}, ISSN={["1873-6270"]}, url={http://inspirehep.net/record/1395973}, DOI={10.1016/j.physrep.2015.12.003}, abstractNote={We review the progress achieved in extracting the properties of hot and dense matter from relativistic heavy ion collisions at the relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory and the large hadron collider (LHC) at CERN. We focus on bulk properties of the medium, in particular the evidence for thermalization, aspects of the equation of state, transport properties, as well as fluctuations and correlations. We also discuss the in-medium properties of hadrons with light and heavy quarks, and measurements of dileptons and quarkonia. This review is dedicated to the memory of Gerald E. Brown.}, journal={PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS}, author={Braun-Munzinger, Peter and Koch, Volker and Schaefer, Thomas and Stachel, Johanna}, year={2016}, month={Mar}, pages={76–126} }
 @article{bluhm_schaefer_2015, title={Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Anisotropic fluid dynamics}, volume={92}, ISSN={["1094-1622"]}, url={http://inspirehep.net/record/1366213}, DOI={10.1103/physreva.92.043602}, abstractNote={We consider the time evolution of a dilute atomic Fermi gas after release from a trapping potential. A common difficulty with using fluid dynamics to study the expansion of the gas is that the theory is not applicable in the dilute corona, and that a naive treatment of the entire cloud using fluid dynamics leads to unphysical results. We propose to remedy this problem by including certain nonhydrodynamic degrees of freedom, in particular anisotropic components of the pressure tensor, in the theoretical description. We show that, using this method, it is possible to describe the crossover from fluid dynamics to ballistic expansion locally. We illustrate the use of anisotropic fluid dynamics by studying the expansion of the dilute Fermi gas at unitarity using different functional forms of the shear viscosity, including a shear viscosity that is solely a function of temperature, $\ensuremath{\eta}\ensuremath{\sim}{(mT)}^{3/2}$, as predicted by kinetic theory in the dilute limit.}, number={4}, journal={PHYSICAL REVIEW A}, author={Bluhm, M. and Schaefer, T.}, year={2015}, month={Oct} }
 @article{behtash_sulejmanpasic_schaefer_uensal_2015, title={Hidden Topological Angles in Path Integrals}, volume={115}, ISSN={["1079-7114"]}, url={http://inspirehep.net/record/1346264}, DOI={10.1103/physrevlett.115.041601}, abstractNote={We demonstrate the existence of hidden topological angles (HTAs) in a large class of quantum field theories and quantum mechanical systems. HTAs are distinct from theta-parameters in the lagrangian. They arise as invariant angle associated with saddle points of the complexified path integral and their descent manifolds (Lefschetz thimbles). Physical effects of HTAs become most transparent upon analytic continuation in n f to non-integer number of flavors, reducing in the integer n f limit to a Z2 valued phase difference between dominant saddles. In N = 1 super Yang-Mills theory we demonstrate the microscopic mechanism for the vanishing of the gluon condensate. The same effect leads to an anomalously small condensate in a QCD-like SU(N) gauge theory with fermions in the two-index representation. The basic phenomenon is that, contrary to folklore, the gluon condensate can receive both positive and negative contributions in a semi-classical expansion. In quantum mechanics, a HTA leads to a difference in semi-classical expansion of integer and half-integer spin particles.}, number={4}, journal={PHYSICAL REVIEW LETTERS}, author={Behtash, Alireza and Sulejmanpasic, Tin and Schaefer, Thomas and Uensal, Mithat}, year={2015}, month={Jul} }
 @inproceedings{schäfer_2014, title={Deconfinement transition at weak coupling in Yang-Mills theory on a torus}, volume={LATTICE2013}, url={http://inspirehep.net/record/1262712}, DOI={10.22323/1.187.0217}, abstractNote={We describe a weak coupling realization of the deconfinement transition in gauge theory compactified on R 3 × S 1 .We consider Yang-Mills theory with a single Weyl fermion of mass m in the adjoint representation of the gauge group.The fermion is subject to periodic boundary conditions, λ (0) = λ (L), where L is the size of the circle S 1 .This theory reduces to thermal Yang-Mills theory in the limit m → ∞.In the limit m → 0 the deconfinement transition can be studied using weak coupling methods.The analysis is based on semi-classical objects characterized by topological and magnetic charges.At leading order the relevant configurations are monopole-instantons and monopole-anti-monopole pairs ("bions").We argue that in the m -L plane the weak coupling transition is continuously connected to the deconfinement transition in pure gauge theory.}, booktitle={PoS}, author={Schäfer, Thomas}, year={2014}, month={Oct}, pages={217} }
 @inproceedings{schäfer_2014, place={Stony Brook , United States}, title={Fermi liquid theory: A brief survey in memory of Gerald E. Brown}, volume={928}, url={http://inspirehep.net/record/1287668}, DOI={10.1016/j.nuclphysa.2014.04.006}, abstractNote={I present a brief review of Fermi liquid theory, and discuss recent work on Fermi liquid theory in dilute neutron matter and cold atomic gases. I argue that renewed interest in transport properties of quantum fluids provides fresh support for Landau's approach to Fermi liquid theory, which is based on kinetic theory rather than effective field theory and the renormalization group. I also discuss work on non-Fermi liquids, in particular dense quark matter.}, booktitle={Nucl.Phys.A}, author={Schäfer, Thomas}, year={2014}, month={Aug}, pages={180–189} }
 @article{schaefer_2014, title={Fluid Dynamics and Viscosity in Strongly Correlated Fluids}, volume={64}, ISSN={["1545-4134"]}, url={http://inspirehep.net/record/1283620}, DOI={10.1146/annurev-nucl-102313-025439}, abstractNote={We review the modern view of fluid dynamics as an effective low-energy, long-wavelength theory of many-body systems at finite temperature. We introduce the concept of a nearly perfect fluid, defined by a ratio η/s of shear viscosity to entropy density of order ℏ/kBor less. Nearly perfect fluids exhibit hydrodynamic behavior at all distances down to the microscopic length scale of the fluid. We summarize arguments that suggest that there is fundamental limit to fluidity, and we review the current experimental situation of measurements of η/s in strongly coupled quantum fluids.}, journal={ANNUAL REVIEW OF NUCLEAR AND PARTICLE SCIENCE, VOL 64}, author={Schaefer, Thomas}, year={2014}, pages={125–148} }
 @article{bluhm_schaefer_2014, title={Medium effects and the shear viscosity of the dilute Fermi gas away from the conformal limit}, volume={90}, ISSN={["1094-1622"]}, url={http://inspirehep.net/record/1321574}, DOI={10.1103/PhysRevA.90.063615}, abstractNote={We study the shear viscosity of a dilute Fermi gas as a function of the scattering length in the vicinity of the unitarity limit. The calculation is based on kinetic theory, which provides a systematic approach to transport properties in the limit in which the fugacity $z=n\lambda^3/2$ is small. Here, $n$ is the density of the gas and $\lambda$ is the thermal wave length of the fermions. At leading order in the fugacity expansion the shear viscosity is independent of density, and the minimum shear viscosity is achieved at unitarity. At the next order medium effects modify the scattering amplitude as well as the quasi-particle energy and velocity. We show that these effects shift the minimum of the shear viscosity to the Bose-Einstein condensation (BEC) side of the resonance, in agreement with the result of recent experiments.}, number={6}, journal={PHYSICAL REVIEW A}, author={Bluhm, M. and Schaefer, T.}, year={2014}, month={Dec} }
 @article{schaefer_2014, title={Second order fluid dynamics for the unitary Fermi gas from kinetic theory}, volume={90}, url={http://inspirehep.net/record/1292847}, DOI={10.1103/PhysRevA.90.043633}, abstractNote={We compute second order transport coefficients of the dilute Fermi gas at unitarity. The calculation is based on kinetic theory and the Boltzmann equation at second order in the Knudsen expansion. The second order transport coefficients describe the shear stress relaxation time, non-linear terms in the strain-stress relation, and non-linear couplings between vorticity and strain. An exact calculation in the dilute limit gives $\tau_R=\eta/P$, where $\tau_R$ is the shear stress relaxation time, $\eta$ is the shear viscosity, and $P$ is pressure. This relation is identical to the result obtained using the Bhatnagar-Gross-Krook (BGK) approximation to the collision term, but other transport coefficients are sensitive to the exact collision integral.}, number={4}, journal={Phys.Rev.A}, author={Schaefer, Thomas}, year={2014}, month={Oct}, pages={043633} }
 @article{schaefer_2014, title={Viscosity spectral function of a scale invariant nonrelativistic fluid from holography}, volume={90}, url={http://inspirehep.net/record/1311648}, DOI={10.1103/PhysRevD.90.106008}, abstractNote={We study the viscosity spectral function of a holographic 2+1 dimensional fluid with Schroedinger symmetry. The model is based on a twisted compactification of $Ads_5\times S_5$. We numerically compute the spectral function of the stress tensor correlator for all frequencies, and analytically study the limits of high and low frequency. We compute the shear viscosity, the viscous relaxation time, and the quasi-normal mode spectrum in the shear channel. We find a number of unexpected results: The high frequency behavior is governed by a fractional 1/3 power law, the viscous relaxation time is negative, and the quasi-normal mode spectrum in the shear channel is not doubled.}, number={10}, journal={Phys.Rev.D}, author={Schaefer, Thomas}, year={2014}, month={Nov}, pages={106008} }
 @article{dusling_schäfer_2013, title={Bulk viscosity and conformal symmetry breaking in the dilute Fermi gas near unitarity}, volume={111}, url={http://inspirehep.net/record/1234416}, DOI={10.1103/PhysRevLett.111.120603}, abstractNote={The dilute Fermi gas at unitarity is scale invariant and its bulk viscosity vanishes. We compute, in the high temperature limit, the leading contribution to the bulk viscosity when the scattering length is not infinite. A measure of scale breaking is provided by the ratio (P-2πħ/3ε)/P, where P is the pressure and E is the energy density. At high temperature this ratio scales as zλ/a, where z is the fugacity, λ is the thermal wavelength, and a is the scattering length. We show that the bulk viscosity ζ scales as the second power of this parameter, ζ~(zλ/a)(2)λ(-3).}, number={12}, journal={Phys.Rev.Lett.}, author={Dusling, Kevin and Schäfer, Thomas}, year={2013}, month={Sep}, pages={120603} }
 @article{schaefer_dusling_2013, title={Bulk viscosity, chemical equilibration and flow at RHIC}, volume={904}, ISSN={["0375-9474"]}, url={http://inspirehep.net/record/1190721}, DOI={10.1016/j.nuclphysa.2013.02.032}, abstractNote={We study the effects of bulk viscosity on p_T spectra and elliptic flow in heavy ion collisions at RHIC. We argue that direct effect of the bulk viscosity on the evolution of the velocity field is small, but corrections to the freezeout distributions can be significant. These effects are dominated by chemical non-equilibration in the hadronic phase. We show that a non-zero bulk viscosity in the range $\zeta/s \lsim 0.05$ improves the description of spectra and flow at RHIC.}, journal={NUCLEAR PHYSICS A}, author={Schaefer, Thomas and Dusling, Kevin}, editor={Ullrich, Thomas and Wyslouch, Bolek and Harris, John W.Editors}, year={2013}, month={May}, pages={393C–396C} }
 @article{adams_carr_schaefer_steinberg_thomas_2013, title={Focus on strongly correlated quantum fluids: From ultracold quantum gases to QCD plasmas}, volume={15}, url={http://inspirehep.net/record/1233002}, DOI={10.1088/1367-2630/15/045022}, abstractNote={The last few years have witnessed a dramatic convergence of three distinct lines of research concerned with different kinds of extreme quantum matter. Two of these involve new quantum fluids that can be studied in the laboratory, ultracold quantum gases and quantum chromodynamics (QCD) plasmas. Even though these systems involve vastly different energy scales, the physical properties of the two quantum fluids are remarkably similar. The third line of research is based on the discovery of a new theoretical tool for investigating the properties of extreme quantum matter, holographic dualties. The main goal of this focus issue is to foster communication and understanding between these three fields. We proceed to describe each in more detail. Ultracold quantum gases offer a new paradigm for the study of nonperturbative quantum many-body physics. With widely tunable interaction strength, spin composition, and temperature, using different hyperfine states one can model spin-1/2 fermions, spin-3/2 fermions, and many other spin structures of bosons, fermions, and mixtures thereof. Such systems have produced a revolution in the study of strongly interacting Fermi systems, for example in the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover region, where a close collaboration between experimentalists and theorists—typical in this field—enabled ground-breaking studies in an area spanning several decades. Half-way through this crossover, when the scattering length characterizing low-energy collisions diverges, one obtains a unitary quantum gas, which is universal and scale invariant. The unitary gas has close parallels in the hydrodynamics of QCD plasmas, where the ratio of viscosity to entropy density is extremely low and comparable to the minimum viscosity conjecture, an important prediction of AdS/CFT (see below). Exciting developments in the thermodynamic and transport properties of strongly interacting Fermi gases are of broad interdisciplinary appeal and include new studies of high temperature superfluidity, viscosity, spin-transport, spin-imbalanced mixtures, and three-component gases, this last having a close parallel to color superconductivity. Another system important for the field of strongly-interacting quantum fluids was revealed by analysis of data from the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory. Despite naive expectations based on asymptotic freedom that the deconfinement of quarks and gluons at high temperatures would lead to a weakly-interacting quark gluon plasma (QGP), the system appeared to be quite strongly coupled. Subsequent estimates of the viscosity-to-entropy ratio suggest that the system is tantalizingly close to the postulated bound from AdS/CFT calculations. The field is quite dynamic at the moment; new measurements are expected from upgraded detectors at RHIC, and an entirely new energy regime is being opened up by heavy ion collisions at the Large Hadron Collider (LHC) at CERN. On the theoretical side, much work remains to be done to extract the precise values of the transport coefficients, and to characterize the nature of quasi-particle excitations in the plasma. Finally, holographic dualities such as anti-de Sitter/conformal field theory (AdS/CFT) have opened a new theoretical window on strongly correlated fluids. Holography relates strongly-interacting quantum many-body systems to weakly-coupled semi-classical gravitational systems, replacing quasiparticles with geometry and translating various difficult questions about quantum fluids into simple and calculable geometric exercises. Already, some of the earliest lessons of holography, such as the conjectural bound on the viscosity-to-entropy ratio, have had a considerable impact on the theoretical and experimental study of strongly correlated fluids, from RHIC to ultracold atoms. More recently, the study of holographic superconductors, non-Fermi liquids and unitary quantum gases has touched off a flurry of interest in holography as a toolkit for studying strongly-correlated many-body systems more generally. Holography also allows us to use results from quantum fluids to study classical and quantum gravity; for example, the phase structure of a quantum many-body system translates into a rich classification of black holes in the dual space–time. Given both the rapid progress in applied holography and the exciting developments in ultracold quantum gases and QCD plasmas discussed above, the time is ripe for new collaborations across traditional lines of specialization. This focus issue explores the convergence between three heretofore separate areas of physics. Over forty research groups have contributed original work, and there will be a review article which complements these advances, overviewing them and presenting them in the context of all three fields and their interconnections. The review concludes with a list of open questions. This sets the tone for the present focus issue; namely, interdisciplinary dialog, openness, innovation, and possibility, an emphasis for which New Journal of Physics, an open-access journal of the highest quality, is especially fitted.}, journal={New J.Phys.}, author={Adams, Allan and Carr, Lincoln D. and Schaefer, Thomas and Steinberg, Peter and Thomas, John E.}, year={2013}, pages={045022} }
 @article{chafin_schaefer_2013, title={Hydrodynamic fluctuations and the minimum shear viscosity of the dilute Fermi gas at unitarity}, volume={87}, ISSN={["1094-1622"]}, url={http://inspirehep.net/record/1184528}, DOI={10.1103/physreva.87.023629}, abstractNote={We study hydrodynamic fluctuations in a non-relativistic fluid. We show that in three dimensions fluctuations lead to a minimum in the shear viscosity to entropy density ratio $\eta/s$ as a function of the temperature. The minimum provides a bound on $\eta/s$ which is independent of the conjectured bound in string theory, $\eta/s \geq \hbar/(4\pi k_B)$, where $s$ is the entropy density. For the dilute Fermi gas at unitarity we find $\eta/s\gsim 0.2\hbar$. This bound is not universal -- it depends on thermodynamic properties of the unitary Fermi gas, and on empirical information about the range of validity of hydrodynamics. We also find that the viscous relaxation time of a hydrodynamic mode with frequency $\omega$ diverges as $1/\sqrt{\omega}$, and that the shear viscosity in two dimensions diverges as $\log(1/ \omega)$.}, number={2}, journal={PHYSICAL REVIEW A}, author={Chafin, Clifford and Schaefer, Thomas}, year={2013}, month={Feb} }
 @article{chafin_schaefer_2013, title={Scale breaking and fluid dynamics in a dilute two-dimensional Fermi gas}, volume={88}, ISSN={["1094-1622"]}, url={http://inspirehep.net/record/1247297}, DOI={10.1103/PhysRevA.88.043636}, abstractNote={We study two observables related to the anomalous breaking of scale invariance in a dilute two dimensional Fermi gas, the frequency shift and damping rate of the monopole mode in a harmonic confinement potential. For this purpose we compute the speed of sound and the bulk viscosity of the two dimensional gas in the high temperature limit. We show that the anomaly in the speed of sound scales as $(2P-\rho c_s^2)/P\sim z/[\log(T/E_B)]^2$, and that the bulk viscosity $\zeta$ scales as $\zeta/\eta \sim z^2/[\log(T/E_B)]^6$. Here, $P$ is the pressure, $c_s^2$ is the speed of sound, $\eta$ is the shear viscosity, $z$ is the fugacity, and $E_B$ is the two-body binding energy. We show that our results are consistent with the experimental results of Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)]. Vogt et al. reported a frequency shift $\delta\omega/\omega$ of the order of a few percent, and a damping rate smaller than the background rate $\Gamma/\omega_0\sim 5%$.}, number={4}, journal={PHYSICAL REVIEW A}, author={Chafin, Clifford and Schaefer, Thomas}, year={2013}, month={Oct} }
 @article{poppitz_schäfer_ünsal_2013, title={Universal mechanism of (semi-classical) deconfinement and θ-dependence for all simple groups}, volume={2013}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP03(2013)087}, DOI={10.1007/jhep03(2013)087}, abstractNote={Using the twisted partition function on $ {{\mathbb{R}}^3} $ × $ {{\mathbb{S}}^1} $ , we argue that the deconfinement phase transition in pure Yang-Mills theory for all simple gauge groups is continuously connected to a quantum phase transition that can be studied in a controlled way. We explicitly consider two classes of theories, gauge theories with a center symmetry, such as SU(N c ) gauge theory for arbitrary N c , and theories without a center symmetry, such as G 2 gauge theory. The mechanism governing the phase transition is universal and valid for all simple groups. The perturbative one-loop potential as well as monopole-instantons generate attraction among the eigenvalues of the Wilson line. This is counter-acted by neutral bions — topological excitations which generate eigenvalue repulsion for all simple groups. The transition is driven by the competition between these three effects. We study the transition in more detail for the gauge groups SU(N c ), N c ≥ 3, and G 2. In the case of G 2 there is no change of symmetry, but the expectation value of the Wilson line exhibits a discontinuity. We also examine the effect of the θ-angle on the phase transition and critical temperature T c (θ). The critical temperature is a multi-branched function, which has a minimum at θ = π as a result of topological interference.}, number={3}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Poppitz, Erich and Schäfer, Thomas and Ünsal, Mithat}, year={2013}, month={Mar} }
 @article{dusling_schaefer_2012, title={Bulk viscosity, particle spectra, and flow in heavy-ion collisions}, volume={85}, ISSN={["1089-490X"]}, url={http://inspirehep.net/record/929470}, DOI={10.1103/physrevc.85.044909}, abstractNote={We study the effects of bulk viscosity on pT spectra and elliptic flow in heavy ion collisions. For this purpose we compute the dissipative correction δf to the single particle distribution functions in leading-log QCD, and in several simplified models. We consider, in particular, the relaxation time approximation and a kinetic model for the hadron resonance gas. We implement these distribution functions in a hydrodynamic simulation of Au + Au collisions at RHIC. We find significant corrections due to bulk viscosity in hadron pT spectra and the differential elliptic flow parameter v2(pT). These corrections are dominated by viscous corrections to the distribution function. We find that the relation between δf and the bulk viscosity is different in the quark gluon plasma and hadronic phases. Reliable bounds on the bulk viscosity require accurate calculations of δf in a hadronic resonance gas. Based on v2 spectra at RHIC we conservatively estimate ζ/s ∼ < 0.05 near freeze–out. We also find that effects of the bulk viscosity on the pT integrated v2 are small.}, number={4}, journal={PHYSICAL REVIEW C}, author={Dusling, Kevin and Schaefer, Thomas}, year={2012}, month={Apr} }
 @article{chao_schaefer_2012, title={Conformal symmetry and non-relativistic second-order fluid dynamics}, volume={327}, ISSN={["1096-035X"]}, url={http://inspirehep.net/record/925068}, DOI={10.1016/j.aop.2012.02.017}, abstractNote={We study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in gradients of the hydrodynamic variables. At zeroth order conformal symmetry implies a constraint on the equation of state, E=2/3 P, where E is the energy density and P is the pressure. At first order, conformal symmetry implies that the bulk viscosity must vanish. We show that at second order conformal invariance requires that two-derivative terms in the stress tensor must be traceless, and that it determines the relaxation of dissipative stresses to the Navier-Stokes form. We verify these results by solving the Boltzmann equation at second order in the gradient expansion. We find that only a subset of the terms allowed by conformal symmetry appear.}, number={7}, journal={ANNALS OF PHYSICS}, author={Chao, Jingyi and Schaefer, Thomas}, year={2012}, month={Jul}, pages={1852–1867} }
 @article{poppitz_schäfer_ünsal_2012, title={Continuity, deconfinement, and (super) Yang-Mills theory}, volume={2012}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP10(2012)115}, DOI={10.1007/JHEP10(2012)115}, abstractNote={We study the phase diagram of SU(2) Yang-Mills theory with one adjoint Weyl fermion on $ {{\mathbb{R}}^3}\times {{\mathbb{S}}^1} $ as a function of the fermion mass m and the compactification scale L. This theory reduces to thermal pure gauge theory as m → ∞ and to circle-compactified (non-thermal) supersymmetric gluodynamics in the limit m → 0. In the m-L plane, there is a line of center-symmetry changing phase transitions. In the limit m → ∞, this transition takes place at L c = 1/T c , where T c is the critical temperature of the deconfinement transition in pure Yang-Mills theory. We show that near m = 0, the critical compactification scale L c can be computed using semi-classical methods and that the transition is of second order. This suggests that the deconfining phase transition in pure Yang-Mills theory is continuously connected to a transition that can be studied at weak coupling. The center-symmetry changing phase transition arises from the competition of perturbative contributions and monopole-instantons that destabilize the center, and topological molecules (neutral bions) that stabilize the center. The contribution of molecules can be computed using supersymmetry in the limit m = 0, and via the Bogomolnyi-Zinn-Justin (BZJ) prescription in non-supersymmetric gauge theory. Finally, we also give a detailed discussion of an issue that has not received proper attention in the context of N = 1 theories — the non-cancellation of nonzero-mode determinants around supersymmetric BPS and KK monopole-instanton backgrounds on $ {{\mathbb{R}}^3}\times {{\mathbb{S}}^1} $ . We explain why the non-cancellation is required for consistency with holomorphy and supersymmetry and perform an explicit calculation of the one-loop determinant ratio.}, number={10}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Poppitz, Erich and Schäfer, Thomas and Ünsal, Mithat}, year={2012}, month={Oct}, pages={115} }
 @inproceedings{schäfer_2012, place={Trento, Italy}, title={Effective Theories of Dense and Very Dense Matter}, volume={852}, url={http://inspirehep.net/record/727206}, DOI={10.1007/978-3-642-27320-9_4}, abstractNote={The exploration of the phase diagram of dense baryonic matter is an area of intense theoretical and experimental activity. Baryonic systems, from dilute neutron matter at low density to superconducting quark matter at high density, exhibit an enormous variety of many-body effects. Despite its simplicity all these phenomena are ultimately described by the lagrangian of QCD.}, booktitle={Lect.Notes Phys.}, author={Schäfer, Thomas}, year={2012}, month={Sep}, pages={193–243} }
 @inproceedings{schäfer_2012, place={Cambridge, United States}, title={Nearly Perfect Fluidity in the Dilute Fermi Gas: An Update}, volume={1441}, url={http://inspirehep.net/record/925597}, DOI={10.1063/1.3700673}, abstractNote={In this contribution we summarize recent results on the transport properties of strongly correlated dilute Fermi gases. We discuss the hydrodynamic equations in the normal phase and present new results on the structure of second order terms in the gradient expansion. We also discuss predictions from kinetic theory, and show how these predictions can be tested using experimental data on elliptic flow. We summarize current constraints on the shear viscosity to entropy density ratio η/s.}, number={1}, booktitle={AIP Conf.Proc.}, author={Schäfer, Thomas}, year={2012}, month={Apr}, pages={761–765} }
 @article{dusling_schaefer_2012, title={Quasiclassical molecular dynamics for the dilute Fermi gas at unitarity}, volume={86}, ISSN={["1094-1622"]}, url={http://inspirehep.net/record/1123691}, DOI={10.1103/physreva.86.063634}, abstractNote={We study the dilute Fermi gas at unitarity using molecular dynamics with an effective quantum potential constructed to reproduce the quantum two-body density matrix at unitarity. Results for the equation of state, the pair correlation function and the shear viscosity are presented. These quantities are well understood in the dilute, high temperature, limit. Using molecular dynamics we determine higher order corrections in the diluteness parameter $n\lambda^3$, where $n$ is the density and $\lambda$ is the thermal de Broglie wave length. In the case of the contact density, which parameterizes the short distance behavior of the correlation function, we find that the results of molecular dynamics interpolates between the truncated second and third order virial expansion, and are in excellent agreement with existing T-matrix calculations. For the shear viscosity we reproduce the expected scaling behavior at high temperature, $\eta\sim 1/\lambda^3$, and we determine the leading density dependent correction to this result.}, number={6}, journal={PHYSICAL REVIEW A}, author={Dusling, K. and Schaefer, T.}, year={2012}, month={Dec} }
 @inbook{schäfer_chafin_2012, title={Scaling Flows and Dissipation in the Dilute Fermi Gas at Unitarity}, volume={836}, url={http://inspirehep.net/record/840910}, DOI={10.1007/978-3-642-21978-8_10}, abstractNote={We describe recent attempts to extract the shear viscosity of the dilute Fermi gas at unitarity from experiments involving scaling flows. A scaling flow is a solution of the hydrodynamic equations that preserves the shape of the density distribution. The scaling flows that have been explored in the laboratory kflccare the transverse expansion from a deformed trap (“elliptic flow”), the expansion from a rotating trap, and collective oscillations. We discuss advantages and disadvantages of the different experiments, and point to improvements of the theoretical analysis that are needed in order to achieve definitive results. A conservative bound based on the current data is that the minimum of the shear viscosity to entropy density ration is $$\eta/s\leq 0.5 \hbar/k_B.$$}, booktitle={Lect.Notes Phys.}, author={Schäfer, Thomas and Chafin, Clifford}, year={2012}, month={Dec}, pages={375–406} }
 @article{schäfer_2012, title={Shear viscosity and damping of collective modes in a two-dimensional Fermi gas}, volume={85}, url={http://inspirehep.net/record/1079476}, DOI={10.1103/PhysRevA.85.033623}, abstractNote={The shear viscosity of a two-dimensional Fermi gas interacting via a short-range potential with scattering length ${a}_{2\mathrm{d}}$ in kinetic theory is computed. It is found that classical kinetic theory predicts that the shear viscosity to entropy density ratio of a strongly interacting two-dimensional gas is comparable to that of the three-dimensional unitary gas. Results are applied to the damping of collective modes of a trapped Fermi gas, and compared to experimental data recently obtained by Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)].}, journal={Phys.Rev.A}, author={Schäfer, Thomas}, year={2012}, month={Nov}, pages={033623} }
 @article{adams_carr_schäfer_steinberg_thomas_2012, title={Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality}, volume={14}, url={http://inspirehep.net/record/1115743}, DOI={10.1088/1367-2630/14/11/115009}, abstractNote={Strongly correlated quantum fluids are phases of matter that are intrinsically quantum mechanical and that do not have a simple description in terms of weakly interacting quasiparticles. Two systems that have recently attracted a great deal of interest are the quark–gluon plasma, a plasma of strongly interacting quarks and gluons produced in relativistic heavy ion collisions, and ultracold atomic Fermi gases, very dilute clouds of atomic gases confined in optical or magnetic traps. These systems differ by 19 orders of magnitude in temperature, but were shown to exhibit very similar hydrodynamic flows. In particular, both fluids exhibit a robustly low shear viscosity to entropy density ratio, which is characteristic of quantum fluids described by holographic duality, a mapping from strongly correlated quantum field theories to weakly curved higher dimensional classical gravity. This review explores the connection between these fields, and also serves as an introduction to the focus issue of New Journal of Physics on ‘Strongly Correlated Quantum Fluids: From Ultracold Quantum Gases to Quantum Chromodynamic Plasmas’. The presentation is accessible to the general physics reader and includes discussions of the latest research developments in all three areas.}, journal={New J.Phys.}, author={Adams, Allan and Carr, Lincoln D. and Schäfer, Thomas and Steinberg, Peter and Thomas, John E.}, year={2012}, month={May}, pages={115009} }
 @inproceedings{schäfer thomas_2012, place={Quito, Ecuador}, title={Transport properties of strongly correlated Fermi fluids}, volume={1423}, url={http://inspirehep.net/record/1231563}, DOI={10.1063/1.3688800}, abstractNote={We present recent results on the transport properties of strongly correlated dilute Fermi gases. We discuss the hydrodynamic equations in the normal phase and summarize new results on the structure of second order terms in the gradient expansion. We also summarize predictions from kinetic theory, and show how these predictions can be tested using experimental data on elliptic flow. We review current constraints on the shear viscosity to entropy density ratio η/s.We present recent results on the transport properties of strongly correlated dilute Fermi gases. We discuss the hydrodynamic equations in the normal phase and summarize new results on the structure of second order terms in the gradient expansion. We also summarize predictions from kinetic theory, and show how these predictions can be tested using experimental data on elliptic flow. We review current constraints on the shear viscosity to entropy density ratio η/s.}, number={1}, booktitle={AIP Conf.Proc.}, author={Schäfer Thomas}, year={2012}, month={Feb}, pages={175–182} }
 @inproceedings{schäfer_2011, title={Elliptic flow and nearly perfect fluidity in dilute Fermi gases}, volume={1343}, url={http://inspirehep.net/record/881619}, DOI={10.1063/1.3574950}, abstractNote={In this contribution we summarize recent progress in understanding the shear viscosity of strongly correlated dilute Fermi gases. We discuss predictions from kinetic theory, and show how these predictions can be tested using recent experimental data on elliptic flow. We find agreement between theory and experiments in the high temperature regime T≫TF, where TF is the the temperature where quantum degeneracy effects become important. In the low temperature regime, T∼TF, the strongest constraints on the shear viscosity come from experimental studies of the damping of collective modes. These experiments indicate that η/s≲0.5h/kB, where η is the shear viscosity and s is the entropy density.}, booktitle={AIP Conf.Proc.}, author={Schäfer, Thomas}, year={2011}, month={Dec}, pages={105–110} }
 @article{dusling_schäfer_2011, title={Elliptic flow of the dilute Fermi gas: From kinetics to hydrodynamics}, volume={84}, url={http://inspirehep.net/record/894277}, DOI={10.1103/PhysRevA.84.013622}, abstractNote={We use the Boltzmann equation in the relaxation-time approximation to study the expansion of a dilute Fermi gas at unitarity. We focus, in particular, on the approach to the hydrodynamic limit. Our main findings are the following: (i) In the regime that has been studied experimentally hydrodynamic effects beyond the Navier-Stokes approximation are small. (ii) Mean-field corrections to the Boltzmann equation are not important. (iii) Experimental data imply that freezeout occurs very late, which means that the relaxation time remains smaller than the expansion time during the entire evolution of the system. (iv) The experimental results also imply that the bulk viscosity is significantly smaller than the shear viscosity of the system.}, journal={Phys.Rev.A}, author={Dusling, Kevin and Schäfer, Thomas}, year={2011}, month={Mar}, pages={013622} }
 @article{braby_chao_schaefer_2011, title={Viscosity spectral functions of the dilute Fermi gas in kinetic theory}, volume={13}, ISSN={["1367-2630"]}, url={http://inspirehep.net/record/878937}, DOI={10.1088/1367-2630/13/3/035014}, abstractNote={We compute the viscosity spectral function of the dilute Fermi gas for different values of the s-wave scattering length a, including the unitarity limit a→∞. We perform the calculation in kinetic theory by studying the response to a non-trivial background metric. We find the expected structure consisting of a diffusive peak in the transverse shear channel and a sound peak in the longitudinal channel. At zero momentum the width of the diffusive peak is ω0≃(2ε)/(3η) where ε is the energy density and η is the shear viscosity. At finite momentum the spectral function approaches the collisionless limit and the width is of the order of ω0∼k(T/m)1/2.}, journal={NEW JOURNAL OF PHYSICS}, author={Braby, Matt and Chao, Jingyi and Schaefer, Thomas}, year={2011}, month={Mar} }
 @article{schäfer_2010, title={Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Free expansion and rotation}, volume={82}, url={http://inspirehep.net/record/865883}, DOI={10.1103/PhysRevA.82.063629}, abstractNote={We investigate the expansion dynamics of a dilute Fermi gas at unitarity in the context of dissipative fluid dynamics. Our aim is to quantify the effects of shear viscosity on the time evolution of the system. We compare exact numerical solutions of the equations of viscous hydrodynamics to various approximations that have been proposed in the literature. Our main findings are (i) shear viscosity leads to characteristic features in the expansion dynamics; (ii) a quantitative description of these effects has to include reheating; (iii) dissipative effects are not sensitive to the equation of state $P(n,T)$ as long as the universal relation $P=\frac{2}{3}\mathcal{E}$ is satisfied; (iv) the expansion dynamics mainly constrains the cloud average of the shear viscosity.}, journal={Phys.Rev.A}, author={Schäfer, Thomas}, year={2010}, month={Aug}, pages={063629} }
 @article{braby_chao_schaefer_2010, title={Thermal conductivity and sound attenuation in dilute atomic Fermi gases}, volume={82}, ISSN={["1094-1622"]}, url={http://inspirehep.net/record/848739}, DOI={10.1103/physreva.82.033619}, abstractNote={We compute the thermal conductivity and sound attenuation length of a dilute atomic Fermi gas in the framework of kinetic theory. Above the critical temperature for superfluidity, T{sub c}, the quasiparticles are fermions, whereas below T{sub c}, the dominant excitations are phonons. We calculate the thermal conductivity in both cases. We find that at unitarity the thermal conductivity {kappa} in the normal phase scales as {kappa}{proportional_to}T{sup 3/2}. In the superfluid phase we find {kappa}{proportional_to}T{sup 2}. At high temperature the Prandtl number, the ratio of the momentum and thermal diffusion constants, is 2/3. The ratio increases as the temperature is lowered. As a consequence we expect sound attenuation in the normal phase just above T{sub c} to be dominated by shear viscosity. We comment on the possibility of extracting the shear viscosity of the dilute Fermi gas at unitarity using measurements of the sound absorption length.}, number={3}, journal={PHYSICAL REVIEW A}, author={Braby, Matt and Chao, Jingyi and Schaefer, Thomas}, year={2010}, month={Sep} }
 @article{braby_chao_schaefer_2010, title={Thermal conductivity of color-flavor-locked quark matter}, volume={81}, ISSN={["1089-490X"]}, url={http://inspirehep.net/record/831992}, DOI={10.1103/physrevc.81.045205}, abstractNote={We compute the thermal conductivity of color-flavor-locked (CFL) quark matter. At temperatures below the scale set by the gap in the quark spectrum, transport properties are determined by collective modes. In this work we focus on the contribution from the lightest modes, the superfluid phonon and the massive neutral kaon. The calculation is done in the framework of kinetic theory, using variational solutions of the linearized Boltzmann equation. We find that the thermal conductivity owing to phonons is kappa{sup (P)}approx1.04x10{sup 26} mu{sub 500}{sup 8}DELTA{sub 50}{sup -6} erg cm{sup -1} s{sup -1} K{sup -1} and the contribution of kaons is kappa{sup (K)}approx2.81x10{sup 21} f{sub p}i{sub ,100}{sup 4}T{sub MeV}{sup 1/2}m{sub 10}{sup -5/2} erg cm{sup -1} s{sup -1} K{sup -1}. These values are smaller than previous estimates but still much larger than (in the case of phonons) or similar to (for kaons) the corresponding values in nuclear matter. From the phonon thermal conductivity we estimate that a CFL quark matter core of a compact star becomes isothermal on a time scale of a few seconds.}, number={4}, journal={PHYSICAL REVIEW C}, author={Braby, Matt and Chao, Jingyi and Schaefer, Thomas}, year={2010}, month={Apr} }
 @article{cao_elliott_joseph_wu_petricka_schafer_thomas_2010, title={Universal Quantum Viscosity in a Unitary Fermi Gas}, volume={331}, ISSN={0036-8075 1095-9203}, url={http://dx.doi.org/10.1126/science.1195219}, DOI={10.1126/science.1195219}, abstractNote={Viscosity studies of an ultracold gas of6Li atoms in two temperature regimes enable comparison with a string theory limit.}, number={6013}, journal={Science}, publisher={American Association for the Advancement of Science (AAAS)}, author={Cao, C. and Elliott, E. and Joseph, J. and Wu, H. and Petricka, J. and Schafer, T. and Thomas, J. E.}, year={2010}, month={Dec}, pages={58–61} }
 @article{rupak_schaefer_2009, title={Density functional theory for non-relativistic fermions in the unitarity limit}, volume={816}, ISSN={["1873-1554"]}, url={http://inspirehep.net/record/783628}, DOI={10.1016/j.nuclphysa.2008.11.004}, abstractNote={We derive an energy density functional for non-relativistic spin one-half fermions in the limit of a divergent two-body scattering length. Using an epsilon expansion around d=4−ε spatial dimensions we compute the coefficient of the leading correction beyond the local density approximation (LDA). In the case of N fermionic atoms trapped in a harmonic potential this correction has the form E=ELDA(1+cs(3N)−2/3), where ELDA is the total energy in LDA approximation. At next-to-leading order in the epsilon expansion we find cs=1.68, which is significantly larger than the result for non-interacting fermions, cs=0.5.}, journal={NUCLEAR PHYSICS A}, author={Rupak, Gautam and Schaefer, Thomas}, year={2009}, month={Jan}, pages={52–64} }
 @inproceedings{schäfer_2009, place={San Diego, United States}, title={In search of the perfect fluid}, volume={1182}, url={http://inspirehep.net/record/824599}, DOI={10.1063/1.3293917}, abstractNote={Shear viscosity measures the amount of internal friction in a simple fluid. In kinetic theory shear viscosity is related to momentum transport by quasi‐particles, and the uncertainty relation implies that the ratio of shear viscosity η to entropy density s is bounded by a constant multiplied by ħ/kB, where ħ is Planck’s constant and kB is Boltzmann’s constant. A specific bound has been proposed on the basis of string theory. In a large class of theories that can be studied using string theory methods the constant is 1/(4π). Experiments at RHIC indicate that η/s of the quark gluon plasma is close to this prediction. We will refer to a fluid that saturates the string theory bound as a perfect fluid. In this contribution we summarizes the theoretical and experimental information on the fluidity of the main classes of strongly interacting quantum fluids.}, number={1}, booktitle={AIP Conf.Proc.}, author={Schäfer, Thomas}, year={2009}, month={Dec}, pages={755–758} }
 @article{schäfer_teaney_2009, title={Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas}, volume={72}, url={http://inspirehep.net/record/818377}, DOI={10.1088/0034-4885/72/12/126001}, abstractNote={Shear viscosity is a measure of the amount of dissipation in a simple fluid. In kinetic theory shear viscosity is related to the rate of momentum transport by quasi-particles, and the uncertainty relation suggests that the ratio of shear viscosity η to entropy density s in units of ℏ/kB is bounded by a constant. Here, ℏ is Planck's constant and kB is Boltzmann's constant. A specific bound has been proposed on the basis of string theory where, for a large class of theories, one can show that η/s ⩾ ℏ/(4πkB). We will refer to a fluid that saturates the string theory bound as a perfect fluid. In this review we summarize theoretical and experimental information on the properties of the three main classes of quantum fluids that are known to have values of η/s that are smaller than ℏ/kB. These fluids are strongly coupled Bose fluids, in particular liquid helium, strongly correlated ultracold Fermi gases and the quark gluon plasma. We discuss the main theoretical approaches to transport properties of these fluids: kinetic theory, numerical simulations based on linear response theory and holographic dualities. We also summarize the experimental situation, in particular with regard to the observation of hydrodynamic behavior in ultracold Fermi gases and the quark gluon plasma.}, journal={Rept.Prog.Phys.}, author={Schäfer, Thomas and Teaney, Derek}, year={2009}, month={Apr}, pages={126001} }
 @misc{alford_schmitt_rajagopal_schaefer_2008, title={Color superconductivity in dense quark matter}, volume={80}, ISSN={["1539-0756"]}, url={http://inspirehep.net/record/762418}, DOI={10.1103/revmodphys.80.1455}, abstractNote={Matter at high density and low temperature is expected to be a color superconductor, which is a degenerate Fermi gas of quarks with a condensate of Cooper pairs near the Fermi surface that induces color Meissner effects. At the highest densities, where the QCD coupling is weak, rigorous calculations are possible, and the ground state is a particularly symmetric state, the color-flavor locked (CFL) phase. The CFL phase is a superfluid, an electromagnetic insulator, and breaks chiral symmetry. The effective theory of the low-energy excitations in the CFL phase is known and can be used, even at more moderate densities, to describe its physical properties. At lower densities the CFL phase may be disfavored by stresses that seek to separate the Fermi surfaces of the different flavors, and comparison with the competing alternative phases, which may break translation and/or rotation invariance, is done using phenomenological models. We review the calculations that underlie these results and then discuss transport properties of several color-superconducting phases and their consequences for signatures of color superconductivity in neutron stars.}, number={4}, journal={REVIEWS OF MODERN PHYSICS}, author={Alford, Mark G. and Schmitt, Andreas and Rajagopal, Krishna and Schaefer, Thomas}, year={2008}, pages={1455–1515} }
 @article{furnstahl_rupak_schäfer_2008, title={Effective Field Theory and Finite Density Systems}, volume={58}, url={http://inspirehep.net/record/776820}, DOI={10.1146/annurev.nucl.58.110707.171142}, abstractNote={ This review gives an overview of effective field theory (EFT) as applied at finite density, with a focus on nuclear many-body systems. Uniform systems with short-range interactions illustrate the ingredients and virtues of many-body EFT; we also survey the varied frontiers of EFT for finite nuclei and nuclear matter. }, journal={Ann.Rev.Nucl.Part.Sci.}, author={Furnstahl, Richard J. and Rupak, Gautam and Schäfer, Thomas}, year={2008}, month={Jan}, pages={1–25} }
 @article{schäfer_2008, title={Euclidean correlation functions in a holographic model of QCD}, volume={77}, url={http://inspirehep.net/record/766482}, DOI={10.1103/PhysRevD.77.126010}, abstractNote={We compute Euclidean coordinate space correlation functions in a holographic model of QCD. We concentrate, in particular, on channels that are related to the $U(1{)}_{A}$ problem, the flavor-singlet axial vector, pseudoscalar meson, and pseudoscalar glueball (topological charge) correlator. We find that even a very simple holographic model defined on a slice of five-dimensional anti-de Sitter space provides a qualitatively correct description of QCD correlation functions. We study the role of anomaly terms, and show that both Euclidean positivity and low energy theorems based on the axial anomaly relation are correctly implemented. We compare the results with expectations from an instanton model of the QCD vacuum.}, journal={Phys.Rev.D}, author={Schäfer, Thomas}, year={2008}, month={Nov}, pages={126010} }
 @article{alford_braby_reddy_schäfer_2007, title={Bulk viscosity due to kaons in color-flavor-locked quark matter}, volume={75}, url={http://inspirehep.net/record/743091}, DOI={10.1103/PhysRevC.75.055209}, abstractNote={We calculate the bulk viscosity of color-superconducting quark matter in the color-flavor-locked (CFL) phase. We assume that the lightest bosons are the superfluid mode H and the kaons K{sup 0} and K{sup +}, and that there is no kaon condensate. We calculate the rate of strangeness-equilibrating processes that convert kaons into superfluid modes, and the resultant bulk viscosity. We find that for oscillations with a timescale of milliseconds, at temperatures T<1 MeV, the CFL bulk viscosity is much less than that of unpaired quark matter, but at higher temperatures the bulk viscosity of CFL matter can become larger.}, journal={Phys.Rev.C}, author={Alford, Mark G. and Braby, Matt and Reddy, Sanjay and Schäfer, Thomas}, year={2007}, month={Jan}, pages={055209} }
 @inproceedings{schäfer_2007, place={Madrid, Spain}, title={Effective field theory and the nuclear many body problem}, volume={31}, url={http://inspirehep.net/record/729014}, DOI={10.1140/epja/i2006-10261-y}, abstractNote={We review many-body calculations of the equation of state of dilute neutron matter in the context of effective-field theories of the nucleon-nucleon interaction.}, booktitle={Eur.Phys.J.A}, author={Schäfer, Thomas}, year={2007}, month={Oct}, pages={403–408} }
 @article{schaefer_2007, place={Frankfurt, Germany}, title={From trapped atoms to liberated quarks}, volume={16}, ISSN={["1793-6608"]}, url={http://inspirehep.net/record/719132}, DOI={10.1142/S0218301307006332}, abstractNote={ We discuss some aspects of cold atomic gases in the unitarity limit that are of interest in connection with the physics of dense hadronic matter. We consider, in particular, the equation of state at zero temperature, the magnitude of the pairing gap, and the phase diagram at non-zero polarization. }, number={3}, journal={INTERNATIONAL JOURNAL OF MODERN PHYSICS E-NUCLEAR PHYSICS}, author={Schaefer, Thomas}, year={2007}, month={Apr}, pages={853–865} }
 @article{gerhold_schäfer_kryjevski_2007, title={Goldstone boson currents in a kaon condensed CFL phase}, volume={75}, url={http://inspirehep.net/record/734511}, DOI={10.1103/PhysRevD.75.054012}, abstractNote={We study the stability of the kaon condensed color-flavor locked (CFL) phase of dense quark matter with regard to the formation of a nonzero Goldstone boson current. In the kaon condensed phase there is an electrically charged fermion which becomes gapless near {mu}{sub s}{sup (1)}{approx_equal}1.35{delta} and a neutral fermion which becomes gapless near {mu}{sub s}{sup (2)}{approx_equal}1.61{delta}. Here, {mu}{sub s}=m{sub s}{sup 2}/(2p{sub F}) is the shift in the Fermi energy due to the strange quark mass m{sub s} and {delta} is the gap in the chiral limit. The transition to the gapless phase is continuous at {mu}{sub s}{sup (1)} and first order at {mu}{sub s}{sup (2)}. We find that the magnetic screening masses are real in the regime {mu}{sub s} {mu}{sub s}{sup (2)}. We show that there is a very weak current instability for {mu}{sub s}>{mu}{sub s}{sup (1)} and a more robust instability in a small window near {mu}{sub s}{sup (2)}. We show that in the Goldstone boson current phase all components of the magnetic screening mass are real. There is a range of values of {mu}{sub s} below 2{delta} in which the magnetic gluon screening masses are imaginary but themore » phase is stable with respect to electrically neutral fluctuations of the gauge field.« less}, journal={Phys.Rev.D}, author={Gerhold, Andreas and Schäfer, Thomas and Kryjevski, Andrei}, year={2007}, month={Dec}, pages={054012} }
 @article{schafer_2007, title={Non-Fermi liquid effective field theory of dense QCD matter}, volume={785}, ISSN={["1873-1554"]}, url={http://inspirehep.net/record/724268}, DOI={10.1016/j.nuclphysa.2006.11.054}, abstractNote={We introduce an effective field theory for quasi-particles in dense QCD matter. Unscreened magnetic gluon exchanges lead to non-Fermi liquid behavior. Non-Fermi liquid effects manifest themselves in low energy Green functions that depend on logarithms and fractional powers of energy. We discuss the validity of some standard theorems of Fermi liquid theory.}, number={1-2}, journal={NUCLEAR PHYSICS A}, author={Schafer, Thomas}, year={2007}, month={Mar}, pages={110C–113C} }
 @article{rupak_schäfer_kryjevski_2007, title={Polarized fermions in the unitarity limit}, volume={75}, url={http://inspirehep.net/record/722805}, DOI={10.1103/PhysRevA.75.023606}, abstractNote={We consider a polarized Fermi gas in the unitarity limit. Results are calculated analytically up to next-to-leading order in an expansion about d=4 spatial dimensions. We find a first order transition from superfluid to normal phase. The critical chemical potential asymmetry for this phase transition is {delta}{mu}{sub c}=(2{mu}/{epsilon})(1-0.467{epsilon}), where {epsilon}=4-d is the expansion parameter and {mu} is the average chemical potential of the two fermion species. Stability of the superfluid phase in the presence of supercurrents is also studied.}, journal={Phys.Rev.A}, author={Rupak, Gautam and Schäfer, Thomas and Kryjevski, Andrei}, year={2007}, month={Jul}, pages={023606} }
 @article{rupak_schäfer_2007, title={Shear viscosity of a superfluid Fermi gas in the unitarity limit}, volume={76}, url={http://inspirehep.net/record/755659}, DOI={10.1103/PhysRevA.76.053607}, abstractNote={We compute the shear viscosity of a superfluid atomic Fermi gas in the unitarity limit. The unitarity limit is characterized by a divergent scattering length between the atoms, and it has been argued that this will result in a very small viscosity. We show that in the low temperature $T$ limit the shear viscosity scales as ${\ensuremath{\xi}}^{5}∕{T}^{5}$, where the universal parameter $\ensuremath{\xi}$ relates the chemical potential and the Fermi energy, $\ensuremath{\mu}=\ensuremath{\xi}{\ensuremath{\epsilon}}_{F}$. Combined with the high temperature expansions of the viscosity our results suggest that the viscosity has a minimum near the critical temperature ${T}_{c}$. A na\"{\i}ve extrapolation indicates that the minimum value of the ratio of viscosity over entropy density is within a factor of $\ensuremath{\sim}5$ of the proposed bound $\ensuremath{\eta}∕s\ensuremath{\ge}\ensuremath{\hbar}∕(4\ensuremath{\pi}{k}_{B})$.}, journal={Phys.Rev.A}, author={Rupak, Gautam and Schäfer, Thomas}, year={2007}, month={Jul}, pages={053607} }
 @article{schäfer_2007, title={The Shear Viscosity to Entropy Density Ratio of Trapped Fermions in the Unitarity Limit}, volume={76}, url={http://inspirehep.net/record/742280}, DOI={10.1103/PhysRevA.76.063618}, abstractNote={We extract the shear viscosity to entropy density ratio $\ensuremath{\eta}/s$ of cold fermionic atoms in the unitarity limit from experimental data on the damping of collective excitations. We find that near the critical temperature $\ensuremath{\eta}/s$ is roughly equal to 1/2 in units of $\ensuremath{\hbar}/{k}_{B}$. With the possible exception of the quark gluon plasma, this value is closer to the conjectured lower bound $1/(4\ensuremath{\pi})$ than any other known liquid.}, journal={Phys.Rev.A}, author={Schäfer, Thomas}, year={2007}, month={Jan}, pages={063618} }
 @inproceedings{schäfer_2007, place={Kyoto, Japan}, title={What atomic liquids can teach us about quark liquids}, volume={168}, url={http://inspirehep.net/record/746392}, DOI={10.1143/PTPS.168.303}, abstractNote={We discuss some aspects of cold atomic Fermi gases in the unitarity limit that are of interest in connection with the physics of quark matter and the quark gluon plasma. We consider, in particular, the equation of state, transport properties, the critical temperature for pair condensation, and the response to a pair breaking stress.}, booktitle={Prog.Theor.Phys.Suppl.}, author={Schäfer, Thomas}, year={2007}, month={Mar}, pages={303–311} }
 @article{lee_schafer_2006, title={Cold dilute neutron matter on the lattice. I. Lattice virial coefficients and large scattering lengths}, volume={73}, ISSN={["1089-490X"]}, url={http://inspirehep.net/record/691674}, DOI={10.1103/PhysRevC.73.015201}, abstractNote={We study cold dilute neutron matter on the lattice using an effective field theory. We work in the unitary limit in which the scattering length is much larger than the interparticle spacing. In this article we focus on the equation of state at temperatures above the Fermi temperature and compare lattice simulations to the virial expansion on the lattice and in the continuum. We find that in the unitary limit lattice discretization errors in the second virial coefficient are significantly enhanced. As a consequence the equation of state does not show the universal scaling behavior expected in the unitary limit. We suggest that scaling can be improved by tuning the second virial coefficient rather than the scattering length.}, number={1}, journal={PHYSICAL REVIEW C}, author={Lee, D and Schafer, T}, year={2006}, month={Jan} }
 @article{lee_schafer_2006, title={Cold dilute neutron matter on the lattice. II. Results in the unitary limit}, volume={73}, ISSN={["1089-490X"]}, url={http://inspirehep.net/record/691675}, DOI={10.1103/PhysRevC.73.015202}, abstractNote={This is the second of two articles that investigate cold dilute neutron matter on the lattice using pionless effective field theory. In the unitary limit, where the effective range is zero and scattering length is infinite, simple scaling relations relate thermodynamic functions at different temperatures. When the second virial coefficient is properly tuned, we find that the lattice results obey these scaling relations. We compute the energy per particle, pressure, spin susceptibility, dineutron correlation function, and an upper bound for the superfluid critical temperature.}, number={1}, journal={PHYSICAL REVIEW C}, author={Lee, D and Schafer, T}, year={2006}, month={Jan} }
 @article{schafer_2006, title={Fermionic quasiparticles in QCD at high baryon density}, volume={774}, ISSN={["1873-1554"]}, url={http://inspirehep.net/record/694037}, DOI={10.1016/j.nuclphysa.2006.06.156}, abstractNote={We study fermionic quasi-particles in QCD at very high baryon density. In the normal quark matter phase unscreened magnetic gluon exchanges lead to non-Fermi liquid behavior. Non-Fermi liquid effects manifest themselves in low energy Green functions that depend on logarithms and fractional powers of energy. In the superfluid phase there is an energy gap for fermionic excitations. Quark mass effects can cause the energy gap to vanish. Gapless fermions in the color flavor locked phase cause an instability towards a state with a non-zero supercurrent.}, journal={NUCLEAR PHYSICS A}, author={Schafer, Thomas}, year={2006}, month={Aug}, pages={877–880} }
 @article{schäfer_schwenzer_2006, title={Low energy dynamics in ultradegenerate QCD matter}, volume={97}, url={http://inspirehep.net/record/701248}, DOI={10.1103/PhysRevLett.97.092301}, abstractNote={We study the low-energy behavior of QCD Green functions in the limit that the baryon chemical potential is much larger than the QCD scale parameter LambdaQCD. We show that there is a systematic low-energy expansion in powers of (omega/m)(1/3), where omega is the energy and m is the screening scale. This expansion is valid even if the effective quark-gluon coupling g is not small. The expansion is purely perturbative in the magnetic regime |k| >> k0. If the external momenta and energies satisfy |k| approximately k0, planar, Abelian ladder diagrams involving the full quark propagator have to be resummed but the corresponding Dyson-Schwinger equations are closed.}, journal={Phys.Rev.Lett.}, author={Schäfer, Thomas and Schwenzer, Kai}, year={2006}, month={Dec}, pages={092301} }
 @article{gerhold_schäfer_2006, title={Meson current in the CFL phase}, volume={73}, url={http://inspirehep.net/record/713489}, DOI={10.1103/PhysRevD.73.125022}, abstractNote={We study the stability of the color-flavor-locked (CFL) phase of dense quark matter with regard to the formation of a nonzero Goldstone boson current. We show that an instability appears in the vicinity of the point {mu}{sub s}={delta} which marks the appearance of gapless fermion modes in the CFL phase. Here, {mu}{sub s}=m{sub s}{sup 2}/(2{mu}) is the shift in chemical potential due to the strange quark mass and {delta} is the gap in the chiral limit. We show that in the Goldstone boson current phase all components of the magnetic screening mass are real. In this work we do not take into account homogeneous kaon condensation. We study the effects of an instanton induced interaction of the magnitude required to suppress kaon condensation.}, journal={Phys.Rev.D}, author={Gerhold, A. and Schäfer, T.}, year={2006}, month={Mar}, pages={125022} }
 @article{schäfer_2006, title={Meson supercurrent state in high density QCD}, volume={96}, url={http://inspirehep.net/record/690156}, DOI={10.1103/PhysRevLett.96.012305}, abstractNote={The ground state of three flavor quark matter at asymptotically large density is believed to be the color-flavor-locked (CFL) phase. At nonasymptotic density the effect of the nonzero strange quark mass cannot be neglected. If the strange quark mass exceeds m(s) approximately m(u)(1/3)delta(2/3), the CFL state becomes unstable toward the formation of a neutral kaon condensate. Recently, several authors discovered that for m(s) approximately (2deltap(F))(1/2) the CFL state contains gapless fermions, and that the gapless modes lead to an instability in current-current correlation functions. Using an effective theory of the CFL state, we demonstrate that this instability can be resolved by the formation of a meson supercurrent, analogous to Migdal's p-wave pion condensate. This state has a nonzero meson current that is canceled by a backflow of gapless fermions.}, journal={Phys.Rev.Lett.}, author={Schäfer, Thomas}, year={2006}, month={Aug}, pages={012305} }
 @inbook{schäfer_2006, place={Seattle, United States}, title={The CFL phase and m$_s$: An Effective field theory approach}, volume={8}, url={http://inspirehep.net/record/711222}, DOI={10.1142/9789812773043_0005}, abstractNote={We study the phase diagram of dense quark matter with an emphasis on the role of the strange quark mass. Our approach is based on two effective field theories (EFTs). The first is an EFT that describes quark quasi-particles near the Fermi surface. This EFT is valid at energies small compared to the chemical potential. The second is an EFT for the Goldstone modes in the paired phase. We find that in response to a non-zero strange quark mass the CFL phase first undergoes a transition to a kaon condensed phase, and then to a gapless phase with a non-zero Goldstone boson current.}, booktitle={Ser.Adv.Quant.Many Body Theor.}, author={Schäfer, Thomas}, year={2006}, month={Feb}, pages={109–134} }
 @article{schäfer_2006, title={The Kohn-Luttinger effect in gauge theories}, volume={74}, url={http://inspirehep.net/record/718431}, DOI={10.1103/PhysRevD.74.054009}, abstractNote={Kohn and Luttinger showed that a many body system of fermions interacting via short range forces becomes superfluid even if the interaction is repulsive in all partial waves. In gauge theories such as QCD the interaction between fermions is long range and the assumptions of Kohn and Luttinger are not satisfied. We show that in a U(1) gauge theory the Kohn-Luttinger phenomenon does not take place. In QCD attractive channels always exist, but there are cases in which the primary pairing channel leaves some fermions ungapped. As an example we consider the unpaired fermion in the 2SC phase of QCD with two flavors. We show that it acquires a very small gap via a mechanism analogous to the Kohn-Luttinger effect. The gap is too small to be phenomenologically relevant.}, journal={Phys.Rev.D}, author={Schäfer, Thomas}, year={2006}, month={Jun}, pages={054009} }
 @article{kryjevski_schafer_2005, title={An effective theory for baryons in the CFL phase}, volume={606}, ISSN={["1873-2445"]}, url={http://inspirehep.net/record/655403}, DOI={10.1016/j.physletb.2004.11.081}, abstractNote={We study the effective field theory for fermions in the color-flavor locked (CFL) phase of high density QCD. The effective theory contains a flavor nonet of baryons interacting with a nonet of pseudoscalar Goldstone bosons as well as a singlet scalar Goldstone boson. The theory is similar to chiral perturbation theory in the one-baryon sector. We explain how to incorporate quark mass terms and study the spectrum as a function of the strange quark mass. Without meson condensation gapless baryon modes appears if the strange quark mass exceeds a critical value ms2/(2pF)=Δ, where pF is the Fermi momentum and Δ is the gap in the chiral limit. We show that kaon condensation leads to a rearrangement of the baryon spectrum and shifts the critical strange quark mass for the appearance of a gapless mode to higher values.}, number={1-2}, journal={PHYSICS LETTERS B}, author={Kryjevski, A and Schafer, T}, year={2005}, month={Jan}, pages={52–58} }
 @article{schafer_kao_cotanch_2005, title={Many body methods and effective field theory}, volume={762}, ISSN={["1873-1554"]}, url={http://inspirehep.net/record/681694}, DOI={10.1016/j.nuclphysa.2005.08.006}, abstractNote={In the framework of pionless nucleon-nucleon effective field theory we study different approximation schemes for the nuclear many body problem. We consider, in particular, ladder diagrams constructed from particle-particle, hole-hole, and particle-hole pairs. We focus on the problem of finding a suitable starting point for perturbative calculations near the unitary limit (k_Fa)->infinity and (k_Fr)-> 0, where k_F is the Fermi momentum, a is the scattering length and r is the effective range. We try to clarify the relationship between different classes of diagrams and the large g and large D approximations, where g is the fermion degeneracy and D is the number of space time dimensions. In the large D limit we find that the energy per particle in the strongly interacting system is 1/2 the result for free fermions.}, number={1-2}, journal={NUCLEAR PHYSICS A}, author={Schafer, T and Kao, CW and Cotanch, SR}, year={2005}, month={Nov}, pages={82–101} }
 @article{lee_schafer_2005, title={Neutron matter on the lattice with pionless effective field theory}, volume={72}, ISSN={["1089-490X"]}, url={http://inspirehep.net/record/665772}, DOI={10.1103/PhysRevC.72.024006}, abstractNote={We study neutron matter by combining pionless effective field theory with non-perturbative lattice methods. The neutron contact interaction is determined by zero temperature scattering data. We simulate neutron matter on the lattice at temperatures 4 and 8 MeV and densities below one-fifth normal nuclear matter density. Our results at different lattice spacings agree with one another and match bubble chain calculations at low densities. The equation of state of pure neutron matter obtained from our simulations agrees quantitatively with variational calculations based on realistic potentials.}, number={2}, journal={PHYSICAL REVIEW C}, author={Lee, D and Schafer, T}, year={2005}, month={Aug} }
 @article{kryjevski_kaplan_schäfer_2005, title={New phases in CFL quark matter}, volume={71}, url={http://inspirehep.net/record/649449}, DOI={10.1103/PhysRevD.71.034004}, abstractNote={We consider $O({\ensuremath{\alpha}}_{s})$ corrections to the squared masses of the pseudo-Goldstone excitations about the ground state of dense quark matter. We show that these contributions tend to destabilize the vacuum, leading to a surprisingly complex phase structure for quark matter as a function of quark mass, even for small ${\ensuremath{\alpha}}_{s}$. In particular we find two new phases of CFL quark matter possibly relevant for the real world, for which ${\overline{\ensuremath{\theta}}}_{\mathrm{Q}\mathrm{C}\mathrm{D}}=\ensuremath{\pi}/2$.}, journal={Phys.Rev.D}, author={Kryjevski, Andrei and Kaplan, David B. and Schäfer, Thomas}, year={2005}, month={Apr}, pages={034004} }
 @inproceedings{schwenzer_schäfer_2005, title={Non Fermi Liquid Effects in Dense Matter and Compact Star Cooling}, url={http://inspirehep.net/record/1599730}, DOI={10.1142/9789812702159_0067}, booktitle={6th International Conference on Strong and Electroweak Matter}, author={Schwenzer, Kai and Schäfer, Thomas}, year={2005}, pages={421–425} }
 @inproceedings{schäfer_2004, title={Effective theory of superfluid quark matter}, url={http://inspirehep.net/record/643845}, DOI={10.1142/9789812702524_0026}, abstractNote={We provide a brief introduction to the high density effective theory of QCD. As an application, we consider the instanton correction to the perturbatively generated gap in the color superconducting phase. We show that the instanton correction becomes large for mu = 1.25 GeV in N_f=2 QCD, and for mu = 750 MeV in N_f=3 QCD with a massive strange quark. We also study some other numerical issues related to the magnitude of the gap. We find, in particular, that a renormalization group improved gap equation does not give results that are substantially different from a gap equation with a fixed coupling.}, booktitle={KIAS-APCTP International Symposium in Astro-Hadron Physics: Compact Stars: Quest for New States of Dense Matter}, author={Schäfer, Thomas}, year={2004}, month={Feb}, pages={330–344} }
 @article{chen_lee_schaefer_2004, title={Inequalities for light nuclei in the Wigner symmetry limit}, volume={93}, ISSN={["1079-7114"]}, url={http://inspirehep.net/record/656802}, DOI={10.1103/physrevlett.93.242302}, abstractNote={Using effective field theory we derive inequalities for light nuclei in the Wigner symmetry limit. This is the limit where isospin and spin degrees of freedom can be interchanged. We prove that the energy of any three-nucleon state is bounded below by the average energy of the lowest two-nucleon and four-nucleon states. We show how this is modified by lowest-order terms breaking Wigner symmetry and prove general energy convexity results for SU(N). We also discuss the inclusion of Wigner-symmetric three- and four-nucleon force terms.}, number={24}, journal={PHYSICAL REVIEW LETTERS}, author={Chen, JW and Lee, D and Schaefer, T}, year={2004}, month={Dec} }
 @article{schafer_zetocha_2004, title={Instantons and the spin of the nucleon}, volume={69}, ISSN={["1550-2368"]}, url={http://inspirehep.net/record/643154}, DOI={10.1103/physrevd.69.094028}, abstractNote={Motivated by measurements of the flavor singlet axial coupling constant of the nucleon in polarized deep inelastic scattering we study the contribution of instantons to Okubo-Zweig-Iizuka rule (OZI) violation in the axial-vector channel. We consider, in particular, the ${f}_{1}\ensuremath{-}{a}_{1}$ meson splitting, the flavor singlet and triplet axial coupling of a constituent quark, and the axial coupling constant of the nucleon. We show that instantons provide a short distance contribution to OZI violating correlation functions which is repulsive in the ${f}_{1}$ meson channel and adds to the flavor singlet three-point function of a constituent quark. We also show that the sign of this contribution is determined by positivity arguments. We compute long distance contributions using numerical simulations of the instanton liquid. We find that the isovector axial coupling constant of a constituent quark is ${(g}_{A}^{3}{)}_{Q}=0.9$ and that of a nucleon is ${g}_{A}^{3}=1.28,$ in good agreement with experiment. The flavor singlet coupling of a quark is close to one, while that of a nucleon is suppressed, ${g}_{A}^{0}=0.77.$ However, this number is larger than the experimental value ${g}_{A}^{0}=(0.28\ensuremath{-}0.41).$}, number={9}, journal={PHYSICAL REVIEW D}, author={Schafer, T and Zetocha, V}, year={2004}, month={May} }
 @article{schäfer_schwenzer_2004, title={Neutrino emission from ungapped quark matter}, volume={70}, url={http://inspirehep.net/record/662070}, DOI={10.1103/PhysRevD.70.114037}, abstractNote={We study neutrino emission from a normal, ungapped, quark phase in the core of a compact star. Neutrino emission from noninteracting quark matter leads to an emissivity that scales as {epsilon}{approx}T{sup 7}. We show that the emissivity is enhanced by a combination of Fermi liquid and non-Fermi liquid effects. Fermi liquid effects lead to an emissivity that scales as {epsilon}{approx}{alpha}{sub s}T{sup 6}, as originally shown by Iwamoto. We demonstrate that non-Fermi liquid effects further enhance the rate, leading to {epsilon}{approx}{alpha}{sub s}{sup 3}T{sup 6}log(m/T){sup 2}, where m is the electric screening scale and m>>T under the conditions found in compact stars. We show, however, that combined with non-Fermi liquid effects in the specific heat the enhancement in the emissivity only leads to a modest reduction in the temperature of the star at late times. Our results confirm existing bounds on the presence of ungapped quark matter in compact stars. We also discuss neutrino emission from superconducting phases with ungapped fermionic excitations.}, journal={Phys.Rev.D}, author={Schäfer, Thomas and Schwenzer, Kai}, year={2004}, month={Oct}, pages={114037} }
 @article{schafer_schwenzer_2004, title={Non-Fermi liquid effects in QCD at high density}, volume={70}, ISSN={["1550-2368"]}, url={http://inspirehep.net/record/649845}, DOI={10.1103/physrevd.70.054007}, abstractNote={We study non-Fermi liquid effects due to the exchange of unscreened magnetic gluons in the normal phase of high density QCD by using an effective field theory. A one-loop calculation gives the well-known result that magnetic gluons lead to a logarithmic enhancement in the fermion self-energy near the Fermi surface. The self-energy is of the form {sigma}({omega}){approx}{omega}{gamma}log({omega}), where {omega} is the energy of the fermion, {gamma}=O(g{sup 2}), and g is the coupling constant. Using an analysis of the Dyson-Schwinger equations we show that, in the weak coupling limit, this result is not modified by higher order corrections even in the regime where the logarithm is large, {gamma}log({omega}){approx}1. We also show that this result is consistent with the renormalization group equation in the high density effective field theory.}, number={5}, journal={PHYSICAL REVIEW D}, author={Schafer, T and Schwenzer, K}, year={2004}, month={Sep} }
 @article{lee_borasoy_schäfer_2004, title={Nuclear lattice simulations with chiral effective field theory}, volume={70}, url={http://inspirehep.net/record/644968}, DOI={10.1103/PhysRevC.70.014007}, abstractNote={We study nuclear and neutron matter by combining chiral effective field theory with nonperturbative lattice methods. In our approach, nucleons and pions are treated as point particles on a lattice. This allows us to probe larger volumes, lower temperatures, and greater nuclear densities than in lattice QCD. The low-energy interactions of these particles are governed by chiral effective theory, and operator coefficients are determined by fitting to zero temperature few-body scattering data. The leading dependence on the lattice spacing can be understood from the renormalization group and absorbed by renormalizing operator coefficients. In this way, we have a realistic simulation of many-body nuclear phenomena with no free parameters, a systematic expansion, and a clear theoretical connection to QCD. We present results for hot neutron matter at temperatures 20-40 MeV and densities below twice the nuclear matter density.}, journal={Phys.Rev.C}, author={Lee, Dean and Borasoy, Bugra and Schäfer, Thomas}, year={2004}, month={Feb}, pages={014007} }
 @article{lee_borasoy_schaefer_2004, title={Nuclear lattice simulations with chiral effective field theory}, volume={70}, number={1}, journal={Physical Review. C, Nuclear Physics}, author={Lee, D. and Borasoy, B. and Schaefer, T.}, year={2004}, pages={014007} }
 @inproceedings{schäfer_2003, title={Effective theory of the color flavor locked phase}, volume={715}, url={http://inspirehep.net/record/594036}, DOI={10.1016/S0375-9474(02)01532-4}, abstractNote={We explain how an effective theory of the CFL phase can be used to study the effect of the strange quark mass on the ground state and the excitation spectrum. We also apply the effective theory to the problem of neutrino emission from a CFL quark core inside a neutron star.}, booktitle={Nucl.Phys.A}, author={Schäfer, Thomas}, year={2003}, month={Aug}, pages={879–882} }
 @article{schafer_2003, title={Hard loops, soft loops, and high density effective field theory}, volume={728}, ISSN={["1873-1554"]}, url={http://inspirehep.net/record/622886}, DOI={10.1016/j.nuclphysa.2003.08.028}, abstractNote={We study several issues related to the use of effective field theories in QCD at large baryon density. We show that the power counting is complicated by the appearance of two scales inside loop integrals. Hard dense loops involve the large scale $\mu^2$ and lead to phenomena such as screening and damping at the scale $g\mu$. Soft loops only involve small scales and lead to superfluidity and non-Fermi liquid behavior at exponentially small scales. Four-fermion operators in the effective theory are suppressed by powers of $1/\mu$, but they get enhanced by hard loops. As a consequence their contribution to the pairing gap is only suppressed by powers of the coupling constant, and not powers of $1/\mu$. We determine the coefficients of four-fermion operators in the effective theory by matching quark-quark scattering amplitudes. Finally, we introduce a perturbative scheme for computing corrections to the gap parameter in the superfluid phase}, number={1-2}, journal={NUCLEAR PHYSICS A}, author={Schafer, T}, year={2003}, month={Dec}, pages={251–271} }
 @article{zetocha_schäfer_2003, title={Instanton contribution to scalar charmonium and glueball decays}, volume={67}, url={http://inspirehep.net/record/604223}, DOI={10.1103/PhysRevD.67.114003}, abstractNote={We study instanton contributions to hadronic decays of the scalar glueball, the pseudoscalar charmonium state ${\ensuremath{\eta}}_{c},$ and the scalar charmonium state ${\ensuremath{\chi}}_{c}.$ Hadronic decays of the ${\ensuremath{\eta}}_{c}$ are of particular interest. The three main decay channels are $K\overline{K}\ensuremath{\pi},\ensuremath{\eta}\ensuremath{\pi}\ensuremath{\pi}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}\ensuremath{\pi},$ each with an unusually large branching ratio $\ensuremath{\sim}5%.$ On the quark level, all three decays correspond to an instanton type vertex $(\overline{c}c)(\overline{s}s)(\overline{d}d)(\ifmmode \bar{u}\else \={u}\fi{}u).$ We show that the total decay rate into three pseudoscalar mesons can be reproduced using an instanton size distribution consistent with phenomenology and lattice results. Instantons correctly reproduce the ratio $B(\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\eta})/B(\ensuremath{\pi}\ensuremath{\pi}{\ensuremath{\eta}}^{\ensuremath{'}})$ but overpredict the ratio $B(K\overline{K}\ensuremath{\pi})/B[\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})].$ We consider the role of scalar resonances and suggest that the decay mechanism can be studied by measuring the angular distribution of decay products.}, journal={Phys.Rev.D}, author={Zetocha, Valeriu and Schäfer, Thomas}, year={2003}, month={Dec}, pages={114003} }
 @article{schafer_2003, title={Instantons and scalar multiquark states: From small to large N-c}, volume={68}, ISSN={["2470-0029"]}, url={http://inspirehep.net/record/628192}, DOI={10.1103/physrevd.68.114017}, abstractNote={We study scalar quark-anti-quark and two-quark-two-anti-quark correlation functions in the instanton liquid model. We show that the instanton liquid supports a light scalar-isoscalar (sigma) meson, and that this state is strongly coupled to both $(\bar{q}q)$ and $(\bar{q}q)^2$. The scalar-isovector $a_0$ meson, on the other hand, is heavy. We also show that these properties are specific to QCD with three colors. In the large $N_c$ limit the scalar-isoscalar meson is not light, and it is mainly coupled to $(\bar{q}q)$.}, number={11}, journal={PHYSICAL REVIEW D}, author={Schafer, T}, year={2003}, month={Dec} }
 @inproceedings{schäfer_2003, title={Loops and power counting in the high density effective field theory}, volume={C030614}, url={http://inspirehep.net/record/630629}, booktitle={eConf}, author={Schäfer, Thomas}, year={2003}, month={Oct}, pages={038} }
 @article{schäfer_2003, title={QCD and the eta-prime mass: Instantons or confinement?}, volume={67}, url={http://inspirehep.net/record/602623}, DOI={10.1103/PhysRevD.67.074502}, abstractNote={We argue that lattice calculations of the $\eta'$ mass in QCD with $N_c=2$ colors performed at non-zero baryon chemical potential can be used to study the mechanism responsible for the mass of the $\eta'$. QCD with two colors is an ideal laboratory because it exhibits confinement, chiral symmetry breaking and a would-be $U(1)_A$ Goldstone boson at all densities. Since the instanton density and the confinement scale vary with density in a very different way, instantons are clearly distinguishable from other possible mechanisms. There is an instanton prediction for the $\eta'$ mass at large density that can be compared to lattice results. The density dependence of the instanton contribution is a simple consequence of the integer topological charge carried by the instanton. We also argue that $N_c=3$ color QCD at finite isospin density can be used in order to study the origin of OZI-violation in the scalar sector.}, journal={Phys.Rev.D}, author={Schäfer, Thomas}, year={2003}, month={Nov}, pages={074502} }
 @inproceedings{schäfer_2003, title={Superdense matter}, volume={60}, url={http://inspirehep.net/record/581739}, DOI={10.1007/BF02705169}, abstractNote={We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss the use of weak coupling methods. We study the phase structure as a function of the number of flavors and their masses. We also introduce effective theories that describe low energy excitations at high baryon density. Finally, we comment on the possibility of kaon condensation at very large baryon density.}, booktitle={Pramana}, author={Schäfer, Thomas}, year={2003}, month={Jan}, pages={697–710} }
 @article{schaefer_2003, title={The RHIC gold rush}, volume={16}, DOI={10.1088/2058-7058/16/6/35}, abstractNote={What happens to ordinary matter as you heat it to higher and higher temperatures, or compress it to greater and greater densities? This simple question underpins a major effort to create extreme conditions in the lab, which has recently taken the shape of the Relativistic Heavy Ion Collider (RHIC). This machine has been colliding gold nuclei since 2000, and has produced tantalizing hints that a new state of matter – the quark–gluon plasma – is created in the reactions. But it has also sparked surprises that are sending researchers back to the drawing board.}, number={6}, journal={Physics World}, author={Schaefer, Thomas}, year={2003}, pages={31–35} }
 @article{schäfer_2003, title={The RHIC gold rush}, volume={16N6}, url={http://inspirehep.net/record/625406}, journal={Phys.World}, author={Schäfer, T.}, year={2003}, pages={31–35} }
 @article{bedaque_schäfer_2002, title={High density quark matter under stress}, volume={697}, url={http://inspirehep.net/record/556611}, DOI={10.1016/S0375-9474(01)01272-6}, abstractNote={We study the effect of SU(3)-flavor breaking on high-density quark matter. We discuss, in particular, a nonzero electron chemical potential and a finite strange-quark mass. We argue that these perturbations trigger pion or kaon condensation. The critical chemical potential behaves as μe∼mmsΔ/pF and the critical strange-quark mass as ms∼m1/3Δ2/3, where m is the light-quark mass, Δ is the gap, and pF is the Fermi momentum. We note that parametrically, both the critical μe and ms2/(2pF) are much smaller than the gap.}, journal={Nucl.Phys.A}, author={Bedaque, Paulo F. and Schäfer, Thomas}, year={2002}, month={May}, pages={802–822} }
 @article{schäfer_2002, title={Instanton effects in QCD at high baryon density}, volume={65}, url={http://inspirehep.net/record/581952}, DOI={10.1103/PhysRevD.65.094033}, abstractNote={We study instanton effects in QCD at very high baryon density. In this regime instantons are suppressed by a large power of $(\Lambda_{QCD}/\mu)$, where $\Lambda_{QCD}$ is the QCD scale parameter and $\mu$ is the baryon chemical potential. Instantons are nevertheless important because they contribute to several physical observables that vanish to all orders in perturbative QCD. We study, in particular, the chiral condensate and its contribution $m_{GB}^2\sim m $ to the masses of Goldstone bosons in the CFL phase of QCD with $N_f=3$ flavors. We find that at densities $\rho\sim (5-10) \rho_0$, where $\rho_0$ is the density of nuclear matter, the result is dominated by large instantons and subject to considerable uncertainties. We suggest that these uncertainties can be addressed using lattice calculations of the instanton density and the pseudoscalar diquark mass in QCD with two colors. We study the topological susceptibility and Witten-Veneziano type mass relations in both $N_c=2$ and $N_c=3$ QCD.}, journal={Phys.Rev.D}, author={Schäfer, Thomas}, year={2002}, month={Jan}, pages={094033} }
 @article{schäfer_2002, title={Instantons in QCD with many colors}, volume={66}, url={http://inspirehep.net/record/587993}, DOI={10.1103/PhysRevD.66.076009}, abstractNote={We study instantons in QCD with many colors. We first discuss a number of qualitative arguments concerning the large ${N}_{c}$ scaling behavior of a random instanton ensemble. We show that most hadronic observables are compatible with standard large ${N}_{c}$ counting rules provided the average instanton size is $O(1)$ and the instanton density is ${O(N}_{c})$ in the large ${N}_{c}$ limit. This is not the case for the topological susceptibility and the mass of the ${\ensuremath{\eta}}^{\ensuremath{'}}.$ For these observables consistency with conventional large ${N}_{c}$ counting requires that fluctuations in the instanton liquid are suppressed compared to Poissonian fluctuations. Using mean field estimates and numerical simulations we show that the required scaling behavior of the instanton density is natural in models in which the instanton density is regularized in terms of a classical repulsive core. We also show that in these models fluctuations of the topological charge are suppressed and that ${m}_{{\ensuremath{\eta}}^{\ensuremath{'}}}^{2}{=O(1/N}_{c}).$ We conclude that the instanton liquid model is not necessarily in conflict with the ${1/N}_{c}$ expansion.}, journal={Phys.Rev.D}, author={Schäfer, Thomas}, year={2002}, month={Jun}, pages={076009} }
 @article{schäfer_2002, title={Mass terms in effective theories of high density quark matter}, volume={65}, url={http://inspirehep.net/record/562459}, DOI={10.1103/PhysRevD.65.074006}, abstractNote={We study the structure of mass terms in the effective theory for quasi-particles in QCD at high baryon density. To next-to-leading order in the $1/p_F$ expansion we find two types of mass terms, chirality conserving two-fermion operators and chirality violating four-fermion operators. In the effective chiral theory for Goldstone modes in the color-flavor-locked (CFL) phase the former terms correspond to effective chemical potentials, while the latter lead to Lorentz invariant mass terms. We compute the masses of Goldstone bosons in the CFL phase, confirming earlier results by Son and Stephanov as well as Bedaque and Sch\"afer. We show that to leading order in the coupling constant $g$ there is no anti-particle gap contribution to the mass of Goldstone modes, and that our results are independent of the choice of gauge.}, journal={Phys.Rev.D}, author={Schäfer, Thomas}, year={2002}, month={Sep}, pages={074006} }
 @article{jaikumar_prakash_schäfer_2002, title={Neutrino emission from Goldstone modes in dense quark matter}, volume={66}, url={http://inspirehep.net/record/583748}, DOI={10.1103/PhysRevD.66.063003}, abstractNote={We calculate neutrino emissivities from the decay and scattering of Goldstone bosons in the color-flavor-locked (CFL) phase of quarks at high baryon density. Interactions in the CFL phase are described by an effective low-energy theory. For temperatures in the tens of keV range, relevant to the long-term cooling of neutron stars, the emissivities involving Goldstone bosons dominate over those involving quarks, because gaps in the CFL phase are $\sim 100$ MeV while the masses of Goldstone modes are on the order of 10 MeV. For the same reason, the specific heat of the CFL phase is also dominated by the Goldstone modes. Notwithstanding this, both the emissivity and the specific heat from the massive modes remain rather small, because of their extremely small number densities. The values of the emissivity and the specific heat imply that the timescale for the cooling of the CFL core in isolation is $\sim 10^{26}$ y, which makes the CFL phase invisible as the exterior layers of normal matter surrounding the core will continue to cool through significantly more rapid processes. If the CFL phase appears during the evolution of a proto-neutron star, neutrino interactions with Goldstone bosons are expected to be significantly more important since temperatures are high enough ($\sim 20-40$ MeV) to admit large number densities of Goldstone modes.}, journal={Phys.Rev.D}, author={Jaikumar, Prashanth and Prakash, Madappa and Schäfer, Thomas}, year={2002}, month={Mar}, pages={063003} }
 @inproceedings{egelhof_alkhazov_andronenko_bauchet_dobrovolsky_fritz_gavrilov_geissel_gross_khanzadeev_et al._2002, title={Nuclear-matter distributions of halo nuclei from elastic proton scattering in inverse kinematics}, url={http://inspirehep.net/record/609988}, DOI={10.1007/978-3-642-55560-2_20}, booktitle={Eur.Phys.J.A}, author={Egelhof, P. and Alkhazov, G.D. and Andronenko, M.N. and Bauchet, A. and Dobrovolsky, A.V. and Fritz, S. and Gavrilov, G.E. and Geissel, H. and Gross, C. and Khanzadeev, A.V. and et al.}, year={2002}, month={Jan}, pages={61–67} }
 @article{schäfer_2002, title={Squeezed quark matter}, volume={5}, url={http://inspirehep.net/record/609568}, journal={APCTP Bull.}, author={Schäfer, T.}, year={2002}, pages={10–12} }
 @inproceedings{schäfer_2002, title={Strange goings on in quark matter}, url={http://inspirehep.net/record/562647}, DOI={10.1142/9789812778352_0034}, abstractNote={We review recent work on how the superfluid state of three flavor quark matter is affected by non-zero quark masses and chemical potentials. The study of hadronic matter at high baryon density has recently attracted a lot of interest. At zero baryon density chiral symmetry is broken by a quark-anti-quark condensate. At high density condensation in the quark-anti-quark channel is suppressed. Instead, attractive interactions in the color anti-symmetric quark-quark channel favor the formation of diquark condensates. As a consequence, cold dense quark matter is expected to be a color superconductor. The symmetry breaking pattern depends on the density, the number of quark flavors, and their masses. A particularly symmetric phase is the color-flavor-locked (CFL) phase of three flavor quark matter. This phase is believed to be the true ground state of ordinary matter at very large density.}, booktitle={6th Workshop on Non-Perturbative Quantum Chromodynamics}, author={Schäfer, Thomas}, year={2002}, month={Sep}, pages={250–256} }
 @inproceedings{schäfer_2002, title={The ground state of strange quark matter}, volume={702}, url={http://inspirehep.net/record/592770}, DOI={10.1016/S0375-9474(02)00701-7}, booktitle={Nucl.Phys.A}, author={Schäfer, T.}, editor={Karsch, F. and Satz, H.Editors}, year={2002}, pages={167–176} }
 @article{schäfer_shuryak_2001, title={Implications of the ALEPH tau lepton decay data for perturbative and nonperturbative QCD}, volume={86}, url={http://inspirehep.net/record/534903}, DOI={10.1103/PhysRevLett.86.3973}, abstractNote={We use ALEPH data on hadronic tau decays in order to calculate Euclidean coordinate space correlation functions in the vector and axial-vector channels. The linear combination V-A receives no perturbative contribution and is quantitatively reproduced by the instanton liquid model. In the case of V+A the instanton calculation is in good agreement with the data once perturbative corrections are included. These corrections clearly show the evolution of alpha(s). We also analyze the range of validity of the operator product expansion (OPE). We conclude that the range of validity of the OPE is limited to x less, similar 0.3 fm, whereas the instanton model describes the data over the entire range.}, journal={Phys.Rev.Lett.}, author={Schäfer, Thomas and Shuryak, Edward V.}, year={2001}, month={Oct}, pages={3973–3976} }
 @article{schäfer_son_stephanov_toublan_verbaarschot_2001, title={Kaon condensation and Goldstone's theorem}, volume={522}, url={http://inspirehep.net/record/561937}, DOI={10.1016/S0370-2693(01)01265-5}, abstractNote={We consider QCD at a nonzero chemical potential for strangeness. At a critical value of the chemical potential equal to the kaon mass, kaon condensation occurs through a continuous phase transition. We show that in the limit of exact isospin symmetry a Goldstone boson with the dispersion relation E∼p2 appears in the kaon condensed phase. At the same time, the number of the Goldstone bosons is less than the number of broken generators. Both phenomena are familiar in nonrelativistic systems. We interpret our results in terms of a Goldstone boson counting rule found previously by Nielsen and Chadha. We also formulate a criterion sufficient for the equality between the number of Goldstone bosons and the number of broken generators.}, journal={Phys.Lett.B}, author={Schäfer, Thomas and Son, D.T. and Stephanov, Misha A. and Toublan, D. and Verbaarschot, J.J.M.}, year={2001}, month={Aug}, pages={67–75} }
 @inproceedings{schäfer_shuryak_2001, title={Phases of QCD at high baryon density}, volume={578}, url={http://inspirehep.net/record/535178}, booktitle={Lect.Notes Phys.}, author={Schäfer, Thomas and Shuryak, Edward V.}, year={2001}, month={Jun}, pages={203–217} }
 @article{schäfer_2001, title={Possible color octet quark anti-quark condensate in the instanton model}, volume={64}, url={http://inspirehep.net/record/553237}, DOI={10.1103/PhysRevD.64.037501}, abstractNote={Inspired by a recent proposal for a Higgs description of QCD we study the possible formation of a color- and flavor-octet quark-antiquark condensate in the instanton liquid model. For this purpose we calculate two-point correlation functions of color-singlet and octet quark-antiquark operators. We find long range order in the standard channel, but not in the color-octet channel. We emphasize that similar calculations in lattice QCD can check whether or not a color-flavor locked Higgs phase is realized in QCD at zero temperature and baryon density.}, journal={Phys.Rev.D}, author={Schäfer, Thomas}, year={2001}, month={Feb}, pages={037501} }
 @inproceedings{schäfer_2000, title={Color superconductivity}, volume={3}, url={http://inspirehep.net/record/509553}, DOI={10.1142/S0217979201005969}, abstractNote={ We discuss recent results on color superconductivity in QCD at large chemical potential. }, booktitle={Int.J.Mod.Phys.B}, author={Schäfer, Thomas}, year={2000}, month={Nov}, pages={186–202} }
 @article{schäfer_2000, title={Gluino condensation in an interacting instanton ensemble}, volume={62}, url={http://inspirehep.net/record/525578}, DOI={10.1103/PhysRevD.62.035013}, abstractNote={We perform a semi-classical study of chiral symmetry breaking and of the spectrum of the Dirac operator in QCD with adjoint fermions. For this purpose we calculate matrix elements of the adjoint Dirac operator between instanton zero modes and study their symmetry properties. We present simulations of the instanton ensemble for different numbers of Majorana fermions in the adjoint representation. These simulations provide evidence that instantons lead to gluino condensation in supersymmetric gluodynamics.}, journal={Phys.Rev.D}, author={Schäfer, Thomas}, year={2000}, month={Mar}, pages={035013} }
 @article{rapp_schäfer_shuryak_velkovsky_2000, title={High density QCD and instantons}, volume={280}, url={http://inspirehep.net/record/498369}, DOI={10.1006/aphy.1999.5991}, abstractNote={Abstract Instantons generate strong nonperturbative interactions between quarks. In vacuum, these interactions lead to chiral symmetry breaking and generate constituent quark masses on the order of 300–400 MeV. The observation that the same forces also provide attraction in the scalar diquark channel leads to the prediction that cold quark matter is a color superconductor, with gaps as large as ∼100 MeV. We provide a systematic treatment of color superconductivity in the instanton model. We show that the structure of the superconductor depends on the number of flavors. In the case of two flavors, we verify the standard scenario, and provide an improved calculation of the mass gap. For three flavors, we show that the ground state is color–flavor locked and calculate the chiral condensate in the high-density phase. We show that as a function of the strange quark mass, there is a sharp transition between the two phases. Finally, we go beyond the mean-field approximation and investigate the role of instanton/anti-instanton molecules, which—in addition to superconducting gap formation—provide a competitive mechanism for chiral restoration at finite density.}, journal={Annals Phys.}, author={Rapp, R. and Schäfer, Thomas and Shuryak, Edward V. and Velkovsky, M.}, year={2000}, month={Apr}, pages={35–99} }
 @article{schäfer_2000, title={Kaon condensation in high density quark matter}, volume={85}, url={http://inspirehep.net/record/529947}, DOI={10.1103/PhysRevLett.85.5531}, abstractNote={We point out that the problem of kaon condensation in dense hadronic matter can be addressed in perturbative QCD. Indeed, perturbative calculations suggest that negative kaons are condensed in high-density quark matter if the presence of electrons is taken into account. This observation sheds new light on the proposal that the low-density hyperon and high-density quark matter phases of QCD are continuously connected.}, journal={Phys.Rev.Lett.}, author={Schäfer, Thomas}, year={2000}, month={Jul}, pages={5531–5534} }
 @article{schäfer_2000, title={Patterns of symmetry breaking in QCD at high baryon density}, volume={575}, url={http://inspirehep.net/record/507972}, DOI={10.1016/S0550-3213(00)00063-8}, abstractNote={We study the structure of QCD at very large baryon density for an arbitrary number of flavors $N_f$. We provide evidence that for any number of flavors larger than $N_f=2$ chiral symmetry remains broken at asymptotically large chemical potential. For $N_c=N_f=3$, chiral symmetry breaking follows the standard pattern $SU(3)_L\times SU(3)_R\to SU(3)$, but for $N_f>3$ unusual patterns emerge. We study the case $N_f=3$ in more detail and calculate the magnitude of the chiral order parameters $<\bar\psi\psi>$ and $<(\bar\psi\psi)^2>$ in perturbative QCD. We show that, asymptotically, $<\bar\psi\psi>^{1/3}$ is much smaller than $<(\bar\psi\psi)^2>^{1/6}$. The result can be understood in terms of an approximate discrete symmetry.}, journal={Nucl.Phys.B}, author={Schäfer, Thomas}, year={2000}, month={Sep}, pages={269–284} }
 @article{schäfer_2000, title={Quark hadron continuity in QCD with one flavor}, volume={62}, url={http://inspirehep.net/record/528194}, DOI={10.1103/PhysRevD.62.094007}, abstractNote={We study QCD with one flavor at finite baryon density. In the limit of very high baryon density the system is expected to be a color superconductor. In the case of one flavor, the order parameter is in a {bar 3} of color and has a total angular momentum of 1. We show that, in weak coupling perturbation theory, the energetically preferred phase exhibits ''color-spin locking''; i.e., the color and spin direction of the condensate are aligned. We discuss the properties of this phase and argue that it shares important features of the hadronic phase at low density. In particular, we find an unbroken rotational symmetry, spin-3/2 quasiparticles, and an unusual mechanism for quark-antiquark condensation. Our results are relevant to three flavor QCD in the regime where the strange quark mass is bigger than the critical value for color-flavor locking. We find that the gaps in this case are on the order of 1 MeV.}, journal={Phys.Rev.D}, author={Schäfer, Thomas}, year={2000}, month={Jun}, pages={094007} }
 @inproceedings{schäfer_1999, title={Color superconductivity: Continuity of quark and hadron matter, the role of the strange quark mass, and perturbative results}, volume={661}, url={http://inspirehep.net/record/506661}, DOI={10.1016/S0375-9474(99)85102-1}, abstractNote={We summarize some recent results on the structure of QCD at very high baryon density.}, booktitle={Nucl.Phys.A}, author={Schäfer, Thomas}, year={1999}, month={May}, pages={621–624} }
 @article{schäfer_wilczek_1999, title={Continuity of quark and hadron matter}, volume={82}, url={http://inspirehep.net/record/479903}, DOI={10.1103/PhysRevLett.82.3956}, abstractNote={We review, clarify, and extend the notion of color-flavor locking. We present evidence that for three degenerate flavors the qualitative features of the color-flavor locked state, reliably predicted for high density, match the expected features of hadronic matter at low density. This provides, in particular, a controlled, weak-coupling realization of confinement and chiral symmetry breaking in this (slight) idealization of QCD.}, journal={Phys.Rev.Lett.}, author={Schäfer, Thomas and Wilczek, Frank}, year={1999}, month={Nov}, pages={3956–3959} }
 @article{schäfer_wilczek_1999, title={High density quark matter and the renormalization group in QCD with two and three flavors}, volume={450}, url={http://inspirehep.net/record/478567}, DOI={10.1016/S0370-2693(99)00162-8}, abstractNote={We consider the most general four fermion operators in QCD for two and three massless flavors and study their renormalization in the vicinity of the Fermi surface. We show that, asymptotically, the largest coupling corresponds to scalar diquark condensation. Asymptotically the direct and iterated (molecular) instanton interactions become equal. We provide simple arguments for the form of the operators that diagonalize the evolution equations. Some solutions of the flow equations exhibit instabilities arising out of purely repulsive interactions.}, journal={Phys.Lett.B}, author={Schäfer, Thomas and Wilczek, Frank}, year={1999}, month={Oct}, pages={325–331} }
 @article{schäfer_wilczek_1999, title={Quark description of hadronic phases}, volume={60}, url={http://inspirehep.net/record/497415}, DOI={10.1103/PhysRevD.60.074014}, abstractNote={We extend our proposal that major universality classes of hadronic matter can be understood, and in favorable cases calculated, directly in the microscopic quark variables, to allow for a splitting between strange and light quark masses. A surprisingly simple but apparently viable picture emerges, featuring essentially three phases, distinguished by whether strangeness is conserved (standard nuclear matter), conserved modulo 2 (hypernuclear matter), or locked to color (color flavor locking). These are separated by sharp phase transitions. There is also, potentially, a quark phase matching hadronic {ital K} condensation. The smallness of the secondary gap in two-flavor color superconductivity corresponds to the disparity between the primary dynamical energy scales of QCD and the much smaller energy scales of nuclear physics. {copyright} {ital 1999} {ital The American Physical Society}}, journal={Phys.Rev.D}, author={Schäfer, Thomas and Wilczek, Frank}, year={1999}, month={Mar}, pages={074014} }
 @article{schäfer_wilczek_1999, title={Superconductivity from perturbative one gluon exchange in high density quark matter}, volume={60}, url={http://inspirehep.net/record/502412}, DOI={10.1103/PhysRevD.60.114033}, abstractNote={We study color superconductivity in QCD at asymptotically large chemical potential. In this limit, pairing is dominated by perturbative one-gluon exchange. We derive the Eliashberg equation for the pairing gap and solve this equation numerically. Taking into account both magnetic and electric gluon exchanges, we find $\Delta\sim g^{-5}\exp(-c/g)$ with $c=3\pi^2/\sqrt{2}$, verifying a recent result by Son. For chemical potentials that are of physical interest, $\mu< 1$ GeV, the calculation ceases to be reliable quantitatively, but our results suggest that the gap can be as large as 100 MeV.}, journal={Phys.Rev.D}, author={Schäfer, Thomas and Wilczek, Frank}, year={1999}, month={Jun}, pages={114033} }
 @article{schäfer_1999, title={Tunneling processes in quantum chromodynamics}, volume={55N9}, url={http://inspirehep.net/record/509672}, journal={Phys.Bl.}, author={Schäfer, Thomas}, year={1999}, pages={52–55} }
 @article{rapp_schäfer_shuryak_velkovsky_1998, title={Diquark Bose condensates in high density matter and instantons}, volume={81}, url={http://inspirehep.net/record/451289}, DOI={10.1103/PhysRevLett.81.53}, abstractNote={Instantons lead to strong correlations between up and down quarks with spin zero and antisymmetric color wave functions. In cold and dense matter, n{sub b}{gt}n{sub c}{approx_equal}1 fm {sup {minus}3} and T{lt}T{sub c}{approximately}50 thinspthinspMeV, these pairs Bose condense, replacing the usual {l_angle}{bar q}q{r_angle} condensate and restoring chiral symmetry. At high density, the ground state is a color superconductor in which diquarks play the role of Cooper pairs. An interesting toy model is provided by QCD with two colors: it has a particle-antiparticle symmetry which relates {l_angle}{bar q}q{r_angle} and {l_angle}qq{r_angle} condensates. {copyright} {ital 1998} {ital The American Physical Society}}, journal={Phys.Rev.Lett.}, author={Rapp, R. and Schäfer, Thomas and Shuryak, Edward V. and Velkovsky, M.}, year={1998}, month={Nov}, pages={53–56} }
 @inproceedings{schäfer_1998, title={Diquark condensation in high density baryon matter}, volume={642}, url={http://inspirehep.net/record/472180}, DOI={10.1016/S0375-9474(98)00497-7}, abstractNote={We argue that cold quark matter is a diquark Bose condensate. The Cooper pairs of QCD are spin-isospin zero, color anti-symmetric quark pairs. For two light flavors, instanton effects lead to gaps on the order of 50 MeV.}, booktitle={Nucl.Phys.A}, author={Schäfer, Thomas}, year={1998}, month={Jun}, pages={45–50} }
 @article{schäfer_1998, title={Instantons and the chiral phase transition at nonzero baryon density}, volume={57}, url={http://inspirehep.net/record/465941}, DOI={10.1103/PhysRevD.57.3950}, abstractNote={We study an interacting ensemble of instantons at a finite baryon chemical potential. We emphasize the importance of fermionic zero modes and calculate the fermion induced interaction between instantons at a nonzero chemical potential. We show that unquenched simulations of the instanton ensemble are feasible in two regimes, for a sufficiently small and for a very large chemical potential. At a very large chemical potential chiral symmetry is restored and the instanton ensemble is dominated by strongly correlated chainlike configurations.}, journal={Phys.Rev.D}, author={Schäfer, Thomas}, year={1998}, month={Aug}, pages={3950–3961} }
 @article{schäfer_shuryak_1998, title={Instantons in QCD}, volume={70}, url={http://inspirehep.net/record/425000}, DOI={10.1103/RevModPhys.70.323}, abstractNote={The authors review the theory and phenomenology of instantons in quantum chromodynamics (QCD). After a general overview, they provide a pedagogical introduction to semiclassical methods in quantum mechanics and field theory. The main part of the review summarizes our understanding of the instanton liquid in QCD and the role of instantons in generating the spectrum of light hadrons. The authors also discuss properties of instantons at finite temperature and how instantons can provide a mechanism for the chiral phase transition. They give an overview of the role of instantons in some other models, in particular low-dimensional sigma models, electroweak theory, and supersymmetric QCD.}, journal={Rev.Mod.Phys.}, author={Schäfer, Thomas and Shuryak, Edward V.}, year={1998}, month={Oct}, pages={323–426} }
 @inproceedings{schäfer_1998, title={QCD at finite baryon density: Instantons and color superconductivity}, volume={638}, url={http://inspirehep.net/record/453694}, DOI={10.1016/S0375-9474(98)00347-9}, abstractNote={Instantons lead to strong correlations for qq with spin and isospin zero and color antisymmetric wave functions. In cold and dense quark matter these correlations can lead to diquark Bose condensation and the ground state is a color superconductor.}, booktitle={Nucl.Phys.A}, author={Schäfer, Thomas}, year={1998}, month={Dec}, pages={511C–514C} }
 @inproceedings{shuryak_schäfer_1997, title={Instantons and chiral symmetry restoration in QCD - like theories}, volume={53}, url={http://inspirehep.net/record/445306}, DOI={10.1016/S0920-5632(96)00691-3}, abstractNote={At finite temperatures it is known that quark-induced interaction lead to formation of instanton-anti-instanton molecules, strongly polarized in time direction. We report first direct simulations of the statistical mechanics of the interacting instanton ensemble at finite temperatures. First of all, they confirmed that molecule formation is driving the chiral phase transition. It happens at T ⋍ 140 MeV (for two flavors) and is second order, while being weak first order if quark masses are as in QCD. We also calculated the behavior of thermodynamics, mesonic susceptibilities and screening masses near the phase transition: inside uncertaintes, all agrees with lattice results. Furthermore, the first order phase transition lines extend further in theories with larger number of flavors Nf: for sufficiently small masses we have found that chiral restoration happens at T = 0 already at Nf = 5.}, booktitle={Nucl.Phys.B Proc.Suppl.}, author={Shuryak, Edward V. and Schäfer, Thomas}, year={1997}, pages={472–474} }
 @article{shuryak_schäfer_1997, title={The QCD vacuum as an instanton liquid}, volume={47}, url={http://inspirehep.net/record/40777}, DOI={10.1146/annurev.nucl.47.1.359}, abstractNote={ ▪ Abstract  We review recent progress in understanding the importance of instanton effects in QCD. Instantons provide a mechanism for quark and gluon condensation, explain the U(1)A anomaly and the appearance of a non-perturbative vacuum energy density. In the framework of the instanton liquid model, a large number of hadronic correlation functions were calculated. The results are in good agreement with both experimental data and lattice simulations. We also review recent results on the phase structure of QCD-like theories. Instantons provide a mechanism for chiral symmetry restoration at finite temperature (or for a large number of quark flavors) connected with the formation of instanton–anti-instanton molecules. }, journal={Ann.Rev.Nucl.Part.Sci.}, author={Shuryak, Edward V. and Schäfer, Thomas}, year={1997}, pages={359–394} }
 @article{schäfer_shuryak_1996, title={Hadronic correlation functions in the interacting instanton liquid}, volume={54}, url={http://inspirehep.net/record/403852}, DOI={10.1103/PhysRevD.54.1099}, abstractNote={In this paper we study hadronic correlation functions in the interacting instanton liquid model, both at zero and nonzero temperature {ital T}. At zero {ital T} we investigate the dependence of the correlators on the instanton ensemble, in particular, the effect of the fermionic determinant. We demonstrate that quark-induced correlations between instantons are important, especially in the repulsive {eta}{sup {prime}} and {delta}-meson channels. We also calculate a large number of mesonic and baryonic correlation functions as a function of temperature. We find three different types of behavior as {ital T}{r_arrow}{ital T}{sub {ital c}}. The vector channels {rho},{ital a}{sub 1},{Delta} show a gradual melting of the resonance contribution and approach free quark behavior near the chiral phase transition. The light pseudoscalars and scalars {pi},{sigma} as well as the nucleon show stable resonance contributions, probably even surviving above {ital T}{sub {ital c}}. Correlation functions in the heavy scalar channels {eta}{sup {prime}},{delta} are enhanced as {ital T}{r_arrow}{ital T}{sub {ital c}}. {copyright} {ital 1996 The American Physical Society.}}, journal={Phys.Rev.D}, author={Schäfer, Thomas and Shuryak, Edward V.}, year={1996}, month={Dec}, pages={1099–1111} }
 @inproceedings{schäfer_1996, title={Progress in instanton liquid calculations}, url={http://inspirehep.net/record/40668}, booktitle={3rd AUP Workshop on QCD: Collisions, Confinement, and Chaos}, author={Schäfer, Thomas}, year={1996}, month={Sep}, pages={333–339} }
 @article{schäfer_1996, title={The Axial anomaly in QCD at finite temperature}, volume={389}, url={http://inspirehep.net/record/422347}, DOI={10.1016/S0370-2693(96)01324-X}, abstractNote={We study flavor mixing and the U(1)A anomaly in QCD at zero and finite temperature. Using the instanton liquid model, we show that the strength of the anomaly is essentially unchanged near the critical temperature for chiral symmetry restoration. We demonstrate that nevertheless chiral symmetry restoration has important consequences for the η and η′. In particular, the strange and non-strange components of the η unmix near Tc. The anomaly does not affect the strange eta, so we expect a light purely strange pseudoscalar near the phase transition.}, journal={Phys.Lett.B}, author={Schäfer, Thomas}, year={1996}, month={Aug}, pages={445–451} }
 @inproceedings{schäfer_1996, title={The Chiral phase transition}, volume={610}, url={http://inspirehep.net/record/421765}, DOI={10.1016/S0375-9474(96)00339-9}, abstractNote={I review the current understanding of the chiral phase transition in QCD, with particular emphasis on recent results in the instanton liquid model.}, booktitle={Nucl.Phys.A}, author={Schäfer, Thomas}, year={1996}, month={Aug}, pages={13C–25C} }
 @article{schäfer_shuryak_1996, title={The Interacting instanton liquid in QCD at zero and finite temperature}, volume={53}, url={http://inspirehep.net/record/399602}, DOI={10.1103/PhysRevD.53.6522}, abstractNote={In this paper we study the statistical mechanics of the instanton liquid in QCD. After introducing the partition function as well as the gauge-field- and quark-induced interactions between instantons, we describe a method to calculate the free energy of the instanton system. We use this method to determine the equilibrium density and the equation of state from numerical simulations of the instanton ensemble in QCD for various numbers of flavors. We find that there is a critical number of flavors above which chiral symmetry is restored in the ground state. In the physical case of two light and one intermediate mass flavors, the system undergoes a chiral phase transition at {ital T}{approx_equal}125 MeV. We show that the mechanism for this transition is a rearrangement of the instanton liquid, going from a disordered, random phase at low temperatures to a strongly correlated, molecular phase at high temperature. We also study the behavior of mesonic susceptibilities near the phase transition. {copyright} {ital 1996 The American Physical Society.}}, journal={Phys.Rev.D}, author={Schäfer, Thomas and Shuryak, Edward V.}, year={1996}, month={Sep}, pages={6522–6542} }
 @article{schäfer_shuryak_1995, title={Can hadrons survive the chiral phase transition?}, volume={356}, url={http://inspirehep.net/record/396060}, DOI={10.1016/0370-2693(95)00835-9}, abstractNote={We study mesonic and baryonic correlation functions in the temporal directions in the vicinity of the critical temperature $T\simeq T_c$ using the instanton liquid model. In this model chiral symmetry restoration is driven by the formation of instanton-antiinstanton molecules. Although we find the signals for all hadronic poles to be drastically reduced, some hadronic states seem to survive the phase transition, as loosely bound $U(N_f)\times U(N_f)$ chiral multiplets in the plasma phase. These states are the $0^+ - 0^-$ mesons $(\pi,\sigma,\eta',\delta)$ and the $N(\frac{1}{2}^+) - N(\frac{1}{2}^-)$ baryons.}, journal={Phys.Lett.B}, author={Schäfer, Thomas and Shuryak, Edward V.}, year={1995}, month={May}, pages={147–152} }
 @article{schäfer_shuryak_1995, title={Glueballs and instantons}, volume={75}, url={http://inspirehep.net/record/378938}, DOI={10.1103/PhysRevLett.75.1707}, abstractNote={Gluonic correlation functions and Bethe-Salpeter amplitudes are calculated in an instanton-based model of the QCD vacuum. We consider both the pure gauge case and the situation for real QCD with two light quark flavors. We show that instantons lead to a strong attractive force in the ${J}^{\mathrm{PC}}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0}^{++}$ channel, which results in the scalar glueball being much smaller than other glueballs. In the ${0}^{\ensuremath{-}+}$ channel the corresponding force is repulsive, and in the ${2}^{++}$ case it is absent. The resulting correlators, masses, coupling constants, and wave functions are compared to the results of lattice simulations.}, journal={Phys.Rev.Lett.}, author={Schäfer, Thomas and Shuryak, Edward V.}, year={1995}, month={Oct}, pages={1707–1710} }
 @article{schäfer_shuryak_verbaarschot_1995, title={The Chiral phase transition and instanton - anti-instanton molecules}, volume={51}, url={http://inspirehep.net/record/373819}, DOI={10.1103/PhysRevD.51.1267}, abstractNote={In this paper we explore the idea that the chiral phase transition in QCD can be described as a transition from a disordered instanton liquid to a strongly correlated phase of polarized instanton--anti-instanton molecules. We calculate the degree of polarization of the molecules as a function of the temperature and show that the resulting [ital T] dependence of the fermion determinant drives the chiral phase transition. We also show how the polarization of the molecules can lead to a nontrivial behavior of the energy density and pressure. Finally, we study the effect of the presence of molecules on the propagation of quarks at [ital T][similar to][ital T][sub [ital c]]. We derive the corresponding effective interaction and find that the strength in the scalar-pseudoscalar channel is four times the strength in the vector--axial-vector channel which agrees with recent lattice QCD simulations. We give results for the quark condensates as well as mesonic and baryonic correlation functions and find that the screening masses'' of chiral partners become equal for [ital T][gt][ital T][sub [ital c]], where we still observe substantial attraction in the scalar-pseudoscalar meson channels.}, journal={Phys.Rev.D}, author={Schäfer, Thomas and Shuryak, Edward V. and Verbaarschot, J.J.M.}, year={1995}, month={May}, pages={1267–1281} }
 @article{schäfer_shuryak_verbaarschot_1994, title={Baryonic correlators in the random instanton vacuum}, volume={412}, url={http://inspirehep.net/record/357158}, DOI={10.1016/0550-3213(94)90497-9}, abstractNote={This is the third paper of a series devoted to a systematic study of QCD correlation functions in the framework of an instanton model for the QCD vacuum. In this paper we concentrate on the quark-quark (diquark) and three quark (baryon) channels. We have found that the quark-quark interaction resembles the one between quarks and antiquarks. Similar to the pion and rho channels, the interaction in the scalar isospin I = 0 and vector I = 1 diquark channels is completely different: the former has a much stronger attractive interaction. As a consequence, the SU(3) octet (nucleon) and decuplet (delta) correlators are also found to be qualitatively different. Using a complete set of all available correlation functions, we determine masses and coupling constants for the nucleon and delta. Our results agree surprisingly well with the first lattice data on point to point correlators.}, journal={Nucl.Phys.B}, author={Schäfer, Thomas and Shuryak, Edward V. and Verbaarschot, J.J.M.}, year={1994}, month={Apr}, pages={143–168} }
 @article{schäfer_shuryak_1994, title={Hadronic wave functions in the instanton model}, volume={50}, url={http://inspirehep.net/record/37115}, DOI={10.1103/PhysRevD.50.478}, abstractNote={In this paper we wish to study hadronic wave functions using an instanton model for the QCD vacuum. The wave functions are defined in terms of gauge-invariant Bethe-Salpeter amplitudes which we have determined numerically using a Monte Carlo simulation of the instanton ensemble. We find that the pion and the proton, as well as the [rho] meson and the [Delta], have very similar wave functions but observe a sizable splitting between mesons or baryons with different spin. We compare our results with data obtained in lattice gauge simulations.}, journal={Phys.Rev.D}, author={Schäfer, Thomas and Shuryak, Edward V.}, year={1994}, month={Jan}, pages={478–485} }
 @inproceedings{schäfer, title={Instantons and the chiral phase transition}, url={http://inspirehep.net/record/390092}, booktitle={1994 Meeting of the American Physical Society, Division of Particles and Fields (DPF 94)}, author={Schäfer, T.}, pages={1311–1313} }
 @article{schäfer_koch_brown_1993, title={Charge symmetry breaking and the neutron proton mass difference}, volume={562}, url={http://inspirehep.net/record/364259}, DOI={10.1016/0375-9474(93)90133-I}, abstractNote={We study the behaviour of the neutron-proton mass difference in the nuclear medium. The main contribution to this quantity from charge symmetry breaking in the meson sector is given by ϱω mixing. In order to include this effect in the QCD sum rules, we extend the sum rules to finite density and discuss the importance of additional sources of isospin breaking which appear at finite density.}, journal={Nucl.Phys.A}, author={Schäfer, Thomas and Koch, V. and Brown, G.E.}, year={1993}, pages={644–658} }
 @article{schäfer_weise_1991, title={A Note on the photoproduction sigma term}, volume={3}, url={http://inspirehep.net/record/327848}, journal={PiN Newslett.}, author={Schäfer, Thomas and Weise, W.}, year={1991}, pages={100–104} }
 @inproceedings{schäfer, title={Neutral pion photoproduction at threshold and explicit chiral symmetry breaking}, url={http://inspirehep.net/record/330763}, booktitle={International Workshop on Pions in Nuclei}, author={Schäfer, T.}, pages={630–639} }
 @article{schäfer_weise_1991, title={Threshold pion photoproduction and chiral models of the nucleon}, volume={531}, url={http://inspirehep.net/record/324976}, DOI={10.1016/0375-9474(91)90739-S}, abstractNote={We present calculations of the chiral and isospin symmetry-breaking corrections to the threshold pion photoproduction amplitude E0+. The calculations are based on two chiral models of the nucleon: the chiral bag model and the non-topological soliton model. We find that ΔE0+ from explicit chiral-symmetry breaking is substantial, but not sufficient to explain the discrepancy between the measured γp → π0p threshold amplitude and its predicted value based on the chiral low-energy theorem.}, journal={Nucl.Phys.A}, author={Schäfer, Thomas and Weise, W.}, year={1991}, pages={520–538} }
 @article{schäfer_weise_1990, title={Neutral pion photoproduction at threshold and explicit chiral symmetry breaking}, volume={250}, url={http://inspirehep.net/record/305620}, DOI={10.1016/0370-2693(90)91144-Z}, abstractNote={We investigate effects of explicit chiral symmetry breaking on the (γ,π0) amplitude at threshold (the photoproduction “sigma”- term) using a chiral bag model of the nucleon. We point out a strong connection between this term and the flavor singlet axial coupling constant gA0 which measures the spin fraction carried by the quarks inside the nucleon. A comparison is made with recent experimental data which show deviations from the standard low energy theorem for photoproduction. The possible origin of this discrepancy is discussed on the basis of our calculations.}, journal={Phys.Lett.B}, author={Schäfer, Thomas and Weise, W.}, year={1990}, pages={6–10} }
 @article{kalmbach_schäfer_biro_mosel_1990, title={Sea effects in the chiral quark soliton model}, volume={513}, url={http://inspirehep.net/record/304127}, DOI={10.1016/0375-9474(90)90401-7}, abstractNote={We have performed a self-consistent calculation including the effects of negative-energy quark states on the meson fields in the framework of the chiral quark soliton model. Using a consequent renormalization of the scalar and pseudoscalar-isovector source densities, we have found that the quarks stabilize the soliton at radii smaller than the ones obtained in earlier calculations. The baryonic charge distribution shrinks to about 0.63 fm as compared to 0.71 fm in the MFA calculations.}, journal={Nucl.Phys.A}, author={Kalmbach, U. and Schäfer, Thomas and Biro, T.S. and Mosel, U.}, year={1990}, pages={621–635} }
 @article{hosaka_schäfer_kalmbach_1990, title={Spin content of the nucleon in a nontopological chiral soliton model}, volume={337}, url={http://inspirehep.net/record/306034}, journal={Z.Phys.A}, author={Hosaka, A. and Schäfer, Thomas and Kalmbach, U.}, year={1990}, pages={447–450} }
 @article{pethick_schaefer_schwenk, title={Bose-Einstein condensates in neutron stars}, url={http://inspirehep.net/record/1384093}, author={Pethick, C.J. and Schaefer, Thomas and Schwenk, A.} }
 @article{schäfer_shuryak, title={Comment on `On the origin of the OZI rule in QCD', by N. Isgur and H. B. Thacker}, url={http://inspirehep.net/record/527989}, author={Schäfer, Thomas and Shuryak, Edward V.} }
 @inproceedings{schäfer, title={From Equilibrium to Transport Properties of Strongly Correlated Fermi Liquids}, url={http://inspirehep.net/record/792492}, DOI={10.1142/9789812838667_0013}, abstractNote={Thomas Scha¨ferDepartment of Physics, North Carolina State University,Raleigh, NC 27695We summarize recent results regarding the equilibrium and non-equilibriumbehavior of cold dilute atomic gases in the limit in which the two body scatter-ing length a goes to infinity. In this limit the system is described by a Galileaninvariant (non-relativistic) conformal field theory. We discuss the low energyeffective lagrangian appropriate to the limit a → ∞, and compute low energycoefficients using an ǫ-expansion. We also show how to combine the effectivelagrangian with kinetic theory in order to compute the shear viscosity, andcompare the kinetic theory predictions to experimental results extracted fromthe damping of collective modes in trapped Fermi gases.Keywords: cold atomic gases, conformal symmetry, shear viscosity}, booktitle={8th Workshop on Continuous Advances in QCD (CAQCD-08)}, author={Schäfer, Thomas}, pages={148–159} }
 @article{schäfer, title={Instantons and Monte Carlo methods in quantum mechanics}, url={http://inspirehep.net/record/663823}, author={Schäfer, Thomas} }
 @inproceedings{schäfer, title={Instantons and the large N(c) limit of QCD}, url={http://inspirehep.net/record/584905}, DOI={10.1142/9789812776914_0004}, abstractNote={We summarize our current understanding of instantons in the large N_c limit of QCD. We also present some recent results from simulations of the instanton liquid in QCD for N_c>3.}, booktitle={The Phenomenology of Large N(c) QCD}, author={Schäfer, Thomas}, pages={42–51} }
 @inproceedings{schäfer, title={Instantons and the large N(c) limit, A.D. 2004}, url={http://inspirehep.net/record/667161}, DOI={10.1142/9789812701725_0003}, abstractNote={We review our current understanding of instanton effects in the large N_c limit of QCD. We argue that the instanton liquid can have a smooth large N_c limit which is in agreement with scaling relations derived from Feynman diagrams. We also discuss certain limits of QCD, like the case of high baryon density, in which the Witten-Veneziano relation can be derived from QCD and is saturated by instantons.}, booktitle={ECT* Workshop on Large Nc QCD 2004}, author={Schäfer, Thomas}, pages={28–45} }
 @inproceedings{schäfer, title={Perfect fluidity in atomic physics}, url={http://inspirehep.net/record/755457}, booktitle={23rd Winter Workshop on Nuclear Dynamics}, author={Schäfer, Thomas} }
 @article{schäfer, title={Phase Structure and Transport Properties of Dense Quark Matter}, url={http://inspirehep.net/record/843010}, author={Schäfer, Thomas} }
 @inproceedings{schäfer, place={Newport News, United States}, title={Phases of QCD}, url={http://inspirehep.net/record/691594}, booktitle={20th Annual Hampton University Graduate Studies Program (HUGS 2005)}, author={Schäfer, Thomas} }
 @phdthesis{schaefer, title={Quantum Chromodynamics: Computational Aspects}, url={http://inspirehep.net/record/1482651}, author={Schaefer, Thomas} }
 @inproceedings{schäfer, title={Quark matter}, url={http://inspirehep.net/record/617865}, booktitle={14th National Nuclear Physics Summer School}, author={Schäfer, Thomas}, pages={185–233} }