Relaxation of the degenerate one-dimensional Fermi gas

TL;DR

This paper investigates how a one-dimensional spin-1/2 Fermi gas relaxes to equilibrium at low temperatures, revealing that spin degeneracy and interaction range significantly influence relaxation rates and transport properties.

Contribution

It provides an exact solution for the linearized relaxation dynamics of a weakly interacting 1D Fermi gas near equilibrium, considering spin degeneracy effects.

Findings

Relaxation rate scales linearly with temperature for short-range interactions.

Spin degeneracy significantly affects the relaxation process.

Exact solutions enable evaluation of transport coefficients.

Abstract

We study how a system of one-dimensional spin-1/2 fermions at temperatures well below the Fermi energy approaches thermal equilibrium. The interactions between fermions are assumed to be weak and are accounted for within the perturbation theory. In the absence of an external magnetic field, spin degeneracy strongly affects relaxation of the Fermi gas. For sufficiently short-range interactions, the rate of relaxation scales linearly with temperature. Focusing on the case of the system near equilibrium, we linearize the collision integral and find exact solution of the resulting relaxation problem. We discuss the application of our results to the evaluation of the transport coefficients of the one-dimensional Fermi gas.