@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{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={A bstract Stochastic fluid dynamics governs the long time tails of hydrodynamic correlation functions, and the critical slowing down of relaxation phenomena in the vicinity of a critical point in the phase diagram. In this work we study the role of multiplicative noise in stochastic fluid dynamics. Multiplicative noise arises from the dependence of transport coefficients, such as the diffusion constants for charge and momentum, on fluctuating hydrodynamic variables. We study long time tails and relaxation in the diffusion of a conserved density (model B), and a conserved density coupled to the transverse momentum density (model H). Careful attention is paid to fluctuation-dissipation relations. We observe that multiplicative noise contributes at the same order as non-linear interactions in model B, but is a higher order correction to the relaxation of a scalar density and the tail of the stress tensor correlation function in model H.}, number={1}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Chao, Jingyi and Schafer, Thomas}, year={2021}, month={Jan} }
 @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{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{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} }