Rate of equilibration of a one-dimensional Wigner crystal

TL;DR

This paper investigates how a one-dimensional Wigner crystal of spinless particles reaches thermal equilibrium, highlighting the role of anharmonicity and umklapp scattering in the equilibration process.

Contribution

It provides a detailed analysis of the equilibration rate in a 1D Wigner crystal considering anharmonic effects and umklapp processes, which was not previously quantified.

Findings

Equilibration rate is exponentially suppressed at low temperatures.

Anharmonicity enables phonon interactions leading to thermalization.

Umklapp scattering is essential for full equilibration.

Abstract

We consider a system of one-dimensional spinless particles interacting via long-range repulsion. In the limit of strong interactions the system is a Wigner crystal, with excitations analogous to phonons in solids. In a harmonic crystal the phonons do not interact, and the system never reaches thermal equilibrium. We account for the anharmonism of the Wigner crystal and find the rate at which it approaches equilibrium. The full equilibration of the system requires umklapp scattering of phonons, resulting in exponential suppression of the equilibration rate at low temperatures.