Viscous Properties of a Degenerate One-Dimensional Fermi Gas

TL;DR

This paper investigates the viscous behavior of a weakly interacting one-dimensional Fermi gas, deriving its bulk viscosity at low temperatures and analyzing the transition to a two-fluid hydrodynamic regime at higher frequencies.

Contribution

It provides the first calculation of the bulk viscosity for a degenerate 1D Fermi gas considering interaction effects on quasiparticles.

Findings

Bulk viscosity derived for low temperatures.

Identification of a frequency threshold for decoupling of excitations.

Calculation of three transport coefficients for the two-fluid regime.

Abstract

We study the viscous properties of a system of weakly interacting spin-$\frac{1}{2}$ fermions in one dimension. Accounting for the effect of interactions on the quasiparticle energy spectrum, we obtain the bulk viscosity of this system at low temperatures. Our result is valid for frequencies that are small compared with the rate of fermion backscattering. For frequencies larger than this exponentially small rate, the excitations of the system become decoupled from the center of mass motion, and the fluid is described by two-fluid hydrodynamics. We calculate the three transport coefficients required to describe viscous dissipation in this regime.