Equilibration of a one-dimensional quantum liquid

TL;DR

This paper reviews recent findings on how one-dimensional quantum liquids, described by Luttinger liquid theory, relax towards equilibrium, highlighting the slow relaxation processes and their impact on transport properties.

Contribution

It provides a phenomenological expression for the relaxation rate based on the excitation spectrum of one-dimensional quantum liquids.

Findings

Relaxation of excitations is exponentially slow at low temperatures.

Backscattering processes significantly affect transport properties.

A new expression for the relaxation rate in terms of the excitation spectrum is derived.

Abstract

We review some of the recent results on equilibration of one-dimensional quantum liquids. The low-energy properties of these systems are described by the Luttinger liquid theory, in which the excitations are bosonic quasiparticles. At low temperatures the relaxation of the gas of excitations toward full equilibrium is exponentially slow. In electronic Luttinger liquids these relaxation processes involve backscattering of electrons and give rise to interesting corrections to the transport properties of one-dimensional conductors. We focus on the phenomenological theory of the equilibration of a quantum liquid and obtain an expression for the relaxation rate in terms of the excitation spectrum.