Thermal relaxation and the complete set of second order transport coefficients for the unitary Fermi gas from kinetic theory

TL;DR

This paper calculates the complete set of second order transport coefficients for the unitary Fermi gas using kinetic theory, extending previous work to include heat flow and confirming a simple relation for thermal relaxation time.

Contribution

It provides the full second order transport coefficients for the unitary Fermi gas, including heat flow terms, based on kinetic theory with exact collision integrals.

Findings

Confirmed the thermal relaxation time relation $ au_ = _ m/(c_PT)$

Extended previous results to include heat flow and fugacity gradients

Calculated all second order transport coefficients for the unitary Fermi gas

Abstract

We compute the complete set of second order transport coefficients of the unitary Fermi gas, a dilute gas of spin 1/2 particles interacting via an $s$-wave interaction tuned to infinite scattering length. The calculation is based on kinetic theory and the Chapman-Enskog method at second order in the Knudsen expansion. We take into account the exact two-body collision integral. We extend previous results on second order coefficients related to shear stress by including terms related to heat flow and gradients of the fugacity. We confirm that the thermal relaxation time is given by the simple estimate $\tau_\kappa = \kappa m/(c_PT)$ even if the full collision kernel is taken into account. Here, $\kappa$ is the thermal conductivity, $m$ is the mass of the particles, $c_P$ is the specific heat at constant pressure, and $T$ is the temperature.