Equilibration of a spinless Luttinger liquid

TL;DR

This paper investigates how a spinless Luttinger liquid in one dimension reaches thermal equilibrium, focusing on high-energy backscattering processes that are beyond standard Luttinger liquid theory, and derives an expression for the equilibration rate.

Contribution

It introduces a method to account for high-energy excitations as mobile impurities and derives a general equilibration rate applicable at any interaction strength.

Findings

Equilibration involves high-energy backscattering processes.

Derived an expression for the equilibration rate in terms of impurity spectrum.

Results are valid across all interaction strengths.

Abstract

We study how a Luttinger liquid of spinless particles in one dimension approaches thermal equilibrium. Full equilibration requires processes of backscattering of excitations which occur at energies of order of the bandwidth. Such processes are not accounted for by the Luttinger liquid theory. We treat the high-energy excitations as mobile impurities and derive an expression for the equilibration rate in terms of their spectrum. Our results apply at any interaction strength.