Equilibration of a one-dimensional Wigner crystal

TL;DR

This paper investigates how a one-dimensional Wigner crystal of spinless electrons relaxes to equilibrium, focusing on phonon Umklapp scattering and the effects of integrability on relaxation rates.

Contribution

It provides a detailed analysis of relaxation mechanisms in a 1D Wigner crystal, highlighting the role of Umklapp scattering and integrability in slow equilibration.

Findings

Relaxation rate depends on phonon Umklapp processes.

In the integrable inverse-square interaction model, relaxation rate is zero.

Non-integrable models exhibit finite relaxation rates.

Abstract

Equilibration of a one-dimensional system of interacting electrons requires processes that change the numbers of left- and right-moving particles. At low temperatures such processes are strongly suppressed, resulting in slow relaxation towards equilibrium. We study this phenomenon in the case of spinless electrons with strong long-range repulsion, when the electrons form a one-dimensional Wigner crystal. We find the relaxation rate by accounting for the Umklapp scattering of phonons in the crystal. For the integrable model of particles with inverse-square repulsion, the relaxation rate vanishes.