Quantum quench and thermalization of one-dimensional Fermi gas via phase space hydrodynamics

TL;DR

This paper uses phase space hydrodynamics to analyze how one-dimensional free Fermi gases thermalize after quantum quenches, revealing power law relaxation behaviors in local observables.

Contribution

It introduces a phase space hydrodynamics framework to study quantum quenches and thermalization in one-dimensional Fermi gases, providing analytical results for relaxation dynamics.

Findings

Local observables exhibit power law relaxation at late times.

A simple rule determines the power law exponent.

Results are observable in experiments with 1D Fermi or Tonk's gases.

Abstract

By exploring a phase space hydrodynamics description of one-dimensional free Fermi gas, we discuss how systems settle down to steady states described by the generalized Gibbs ensembles through quantum quenches. We investigate time evolutions of the Fermions which are trapped in external potentials or a circle for a variety of initial conditions and quench protocols. We analytically compute local observables such as particle density and show that they always exhibit power law relaxation at late times. We find a simple rule which determines the power law exponent. Our findings are, in principle, observable in experiments in an one dimensional free Fermi gas or Tonk's gas (Bose gas with infinite repulsion).