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

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.