Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Anisotropic fluid dynamics

TL;DR

This paper introduces anisotropic fluid dynamics to accurately model the expansion of a dilute Fermi gas at unitarity, effectively bridging the gap between hydrodynamic and ballistic regimes by including non-hydrodynamic degrees of freedom.

Contribution

The authors develop a modified fluid dynamic framework incorporating anisotropic pressure components to better describe dilute Fermi gas expansion, especially in the dilute corona.

Findings

Successfully describes the crossover from fluid to ballistic expansion.

Demonstrates the method with different shear viscosity models.

Aligns theoretical predictions with kinetic theory in dilute limit.

Abstract

We consider the time evolution of a dilute atomic Fermi gas after release from a trapping potential. A common difficulty with using fluid dynamics to study the expansion of the gas is that the theory is not applicable in the dilute corona, and that a naive treatment of the entire cloud using fluid dynamics leads to unphysical results. We propose to remedy this problem by including certain non-hydrodynamic degrees of freedom, in particular anisotropic components of the pressure tensor, in the theoretical description. We show that, using this method, it is possible to describe the crossover from fluid dynamics to ballistic expansion locally. We illustrate the use of anisotropic fluid dynamics by studying the expansion of the dilute Fermi gas at unitarity using different functional forms of the shear viscosity, including a shear viscosity which is solely a function of temperature, $\eta\sim (mT)^{3/2}$, as predicted by kinetic theory in the dilute limit.