Second order fluid dynamics for the unitary Fermi gas from kinetic theory

Abstract

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.

arXiv comment22 pages, no figures. v2: Minor revisions, to appear in Phys Rev A

References in corpus (40)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Observation of a Strongly-Interacting Degenerate Fermi Gas of Atoms
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas
• Collective excitations of a degenerate gas at the BEC-BCS crossover
• Exploring the Thermodynamics of a Universal Fermi Gas
• Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas
• Universal Quantum Viscosity in a Unitary Fermi Gas
• Heating up Galilean holography
• Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality
• Feynman diagrams versus Fermi-gas Feynman emulator
• Expansion of an interacting Fermi gas
• Viscosity and scale invariance in the unitary Fermi gas
• Second order hydrodynamic coefficients from kinetic theory
• Vanishing bulk viscosities and conformal invariance of unitary Fermi gas
• Breakdown of Hydrodynamics in the Radial Breathing Mode of a Strongly-Interacting Fermi Gas
• Viscous relaxation and collective oscillations in a trapped Fermi gas near the unitarity limit
• The Shear Viscosity to Entropy Density Ratio of Trapped Fermions in the Unitarity Limit
• Shear viscosity of a superfluid Fermi gas in the unitarity limit
• Shear viscosity and damping for a Fermi gas in the unitarity limit
• Viscosity and Thermal Relaxation for a resonantly interacting Fermi gas
• Fluid Dynamics and Viscosity in Strongly Correlated Fluids
• Observation of conformal symmetry breaking and scale invariance in expanding Fermi gases
• Anomalous minimum in the shear viscosity of a Fermi gas
• Current response, structure factor and hydrodynamic quantities of a two- and three-dimensional Fermi gas from the operator-product expansion
• Thermal Conductivity and Sound Attenuation in Dilute Atomic Fermi Gases
• Cold Strongly Coupled Atoms Make a Near-perfect Liquid
• Frequency and damping of the Scissors Mode of a Fermi gas
• Observation of a quenched moment of inertia in a rotating strongly interacting Fermi gas
• Quantum critical transport in the unitary Fermi gas
• Shear Viscosity of a Unitary Fermi Gas
• Perfect Fluids and Bad Metals: Transport Analogies Between Ultracold Fermi Gases and High $T_c$ Superconductors
• The temperature evolution of the shear viscosity in a unitary Fermi gas
• Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Free expansion and rotation
• Scaling Flows and Dissipation in the Dilute Fermi Gas at Unitarity
• Viscosity spectral functions of the dilute Fermi gas in kinetic theory
• Conformal symmetry and non-relativistic second order fluid dynamics
• Establishing Conservation Laws in Pair Correlated Many Body theories: T matrix Approaches
• Quasiclassical molecular dynamics for the dilute Fermi gas at unitarity

Cited by in corpus (8)

• Fluid Dynamics and Viscosity in Strongly Correlated Fluids
• Model-independent determination of the shear viscosity of a trapped unitary Fermi gas: Application to high temperature data
• Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Anisotropic fluid dynamics
• Quantum critical thermal transport in the unitary Fermi gas
• Mesoscopic dynamics of fermionic cold atoms ---Quantitative analysis of transport coefficients and relaxation times---
• Viscosity spectral function of a scale invariant non-relativistic fluid from holography
• Higher-Harmonic Collective Modes in a Trapped Gas from Second-Order Hydrodynamics
• Dispersion of first sound in a weakly interacting ultracold Fermi liquid