Elliptic flow of the dilute Fermi gas: From kinetics to hydrodynamics

TL;DR

This paper investigates the expansion dynamics of a dilute Fermi gas at unitarity using the Boltzmann equation, highlighting the dominance of hydrodynamic behavior and minimal mean field effects, with implications for viscosity and freezeout timing.

Contribution

It demonstrates that hydrodynamic effects beyond Navier-Stokes are minimal, mean field corrections are negligible, and provides insights into viscosity and freezeout in the system.

Findings

Hydrodynamic effects beyond Navier-Stokes are small.

Mean field corrections are not significant.

Bulk viscosity is much smaller than shear viscosity.

Abstract

We use the Boltzmann equation in the relaxation time approximation to study the expansion of a dilute Fermi gas at unitarity. We focus, in particular, on the approach to the hydrodynamic limit. Our main finding are: i) In the regime that has been studied experimentally hydrodynamic effects beyond the Navier-Stokes approximation are small, ii) mean field corrections to the Boltzmann equation are not important, iii) experimental data imply that freezeout occurs very late, that means that the relaxation time remains smaller than the expansion time during the entire evolution of the system, iv) the experimental results also imply that the bulk viscosity is significantly smaller than the shear viscosity of the system.