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

TL;DR

This paper calculates second order transport coefficients for the unitary Fermi gas using kinetic theory, providing exact results for shear stress relaxation time and insights into non-linear fluid dynamics.

Contribution

It offers the first exact calculation of second order transport coefficients for the dilute Fermi gas at unitarity from kinetic theory.

Findings

Shear stress relaxation time $ au_R = rac{ ext{eta}}{ ext{P}}$ in the dilute limit

Exact calculation matches BGK approximation for $ au_R$

Other coefficients depend on the precise collision integral

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.