@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{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{nahrgang_bluhm_schafer_bass_2017, title={Baryon number diffusion with critical fluctuations}, volume={967}, journal={Nuclear Physics. A}, author={Nahrgang, M. and Bluhm, M. and Schafer, T. and Bass, S. A.}, year={2017}, 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} }
 @article{martinez_schafer_2017, title={Hydrodynamic tails and a fluctuation bound on the bulk viscosity}, volume={96}, number={6}, journal={Physical Review A}, author={Martinez, M. and Schafer, T.}, year={2017} }
 @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} }
 @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{schafer_2016, title={Generalized theory of diffusion based on kinetic theory}, volume={94}, number={4}, journal={Physical Review A}, author={Schafer, T.}, year={2016} }
 @article{schafer_2014, title={Fermi liquid theory: A brief survey in memory of Gerald E. Brown}, volume={928}, journal={Nuclear Physics. A}, author={Schafer, T.}, year={2014}, pages={180–189} }
 @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{schafer_2014, title={Second-order fluid dynamics for the unitary Fermi gas from kinetic theory}, volume={90}, number={4}, journal={Physical Review. A}, author={Schafer, T.}, year={2014} }
 @article{schafer_2014, title={Viscosity spectral function of a scale invariant nonrelativistic fluid from holography}, volume={90}, number={10}, journal={Physical Review. D, Particles, Fields, Gravitation, and Cosmology}, author={Schafer, T.}, year={2014} }
 @article{dusling_schafer_2013, title={Bulk viscosity and conformal symmetry breaking in the dilute fermi gas near unitarity}, volume={111}, number={12}, journal={Physical Review Letters}, author={Dusling, K. and Schafer, T.}, year={2013} }
 @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} }
 @inproceedings{schafer_2012, title={Nearly perfect fluidity in the dilute fermi gas: An update}, volume={1441}, booktitle={19th particles and nuclei international conference (panic11)}, author={Schafer, T.}, year={2012}, pages={761–765} }
 @article{schafer_2012, title={Shear viscosity and damping of collective modes in a two-dimensional Fermi gas}, volume={85}, number={3}, journal={Physical Review. A}, author={Schafer, T.}, year={2012} }
 @inproceedings{schafer_2012, title={Transport properties of strongly correlated fermi fluids}, volume={1423}, booktitle={Ix latin american symposium on nuclear physics and applications}, author={Schafer, T.}, year={2012} }
 @article{schafer_2011, title={Elliptic flow and nearly perfect fluidity in dilute Fermi gases}, volume={1343}, journal={Ix international conference on quark confinement and the hadron spectrum (qchs ix)}, author={Schafer, T.}, year={2011}, pages={105–110} }
 @article{dusling_schafer_2011, title={Elliptic flow of the dilute Fermi gas: From kinetics to hydrodynamics}, volume={84}, number={1}, journal={Physical Review. A}, author={Dusling, K. and Schafer, T.}, year={2011} }
 @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{schafer_2010, title={Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Free expansion and rotation}, volume={82}, number={6}, journal={Physical Review. A}, author={Schafer, T.}, year={2010} }
 @misc{schafer_teaney_2009, title={Nearly perfect fluidity: From cold atomic gases to hot quark gluon plasmas}, volume={72}, number={12}, journal={Reports on Progress in Physics}, author={Schafer, T. and Teaney, D.}, year={2009} }
 @misc{furnstahl_rupak_schafer_2008, title={Effective field theory and finite-density systems}, volume={58}, journal={Annual Review of Nuclear and Particle Science}, author={Furnstahl, R. J. and Rupak, G. and Schafer, T.}, year={2008}, pages={1–25} }
 @article{schafer_2008, title={Euclidean correlation functions in a holographic model of QCD}, volume={77}, number={12}, journal={Physical Review. D, Particles, Fields, Gravitation, and Cosmology}, author={Schafer, T.}, year={2008} }
 @article{alford_braby_reddy_schafer_2007, title={Bulk viscosity due to kaons in color-flavor-locked quark matter}, volume={75}, number={5}, journal={Physical Review. C, Nuclear Physics}, author={Alford, M. G. and Braby, M. and Reddy, S. and Schafer, T.}, year={2007} }
 @article{schafer_2007, title={Effective-field theory and the nuclear many-body problem}, volume={31}, number={4}, journal={European Physical Journal. A, Hadrons and Nuclei}, author={Schafer, T.}, year={2007}, 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_schafer_kryjevski_2007, title={Goldstone boson currents in a kaon condensed color-flavor locked phase}, volume={75}, number={5}, journal={Physical Review. D, Particles, Fields, Gravitation, and Cosmology}, author={Gerhold, A. and Schafer, T. and Kryjevski, A.}, year={2007} }
 @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_schafer_kryjevski_2007, title={Polarized fermions in the unitarity limit}, volume={75}, number={2}, journal={Physical Review. A}, author={Rupak, G. and Schafer, T. and Kryjevski, A.}, year={2007} }
 @article{schafer_2007, title={Ratio of shear viscosity to entropy density for trapped fermions in the unitarity limit}, volume={76}, number={6}, journal={Physical Review. A}, author={Schafer, T.}, year={2007} }
 @article{rupak_schafer_2007, title={Shear viscosity of a superfluid Fermi gas in the unitarity limit}, volume={76}, number={5}, journal={Physical Review. A}, author={Rupak, G. and Schafer, T.}, year={2007} }
 @article{schafer_2007, title={What atomic liquids can teach us about quark liquids}, number={168}, journal={Progress of Theoretical Physics. Supplement}, author={Schafer, T.}, year={2007}, 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{schafer_2006, title={Kohn-Luttinger effect in gauge theories}, volume={74}, number={5}, journal={Physical Review. D, Particles and Fields}, author={Schafer, T.}, year={2006} }
 @article{schafer_schwenzer_2006, title={Low-energy dynamics in ultradegenerate QCD matter}, volume={97}, number={9}, journal={Physical Review Letters}, author={Schafer, T. and Schwenzer, K.}, year={2006} }
 @article{schafer_2006, title={Meson supercurrent state in high-density QCD}, volume={96}, number={1}, journal={Physical Review Letters}, author={Schafer, T.}, year={2006} }
 @article{kryjevski_kaplan_schafer_2005, title={New phases in color-flavor-locked quark matter}, volume={71}, number={3}, journal={Physical Review. D, Particles and Fields}, author={Kryjevski, A. and Kaplan, D. B. and Schafer, T.}, year={2005} }