Relaxation of weakly interacting electrons in one dimension

TL;DR

This paper investigates how weakly interacting electrons in one dimension relax, focusing on decay rates of single-electron excitations considering nonlinear dispersion and different Coulomb interactions, revealing temperature-dependent relaxation mechanisms.

Contribution

It provides a detailed calculation of electron relaxation rates in 1D systems with weak interactions, incorporating nonlinear dispersion and Coulomb interaction effects, which was not thoroughly addressed before.

Findings

Decay rates depend on Coulomb interaction type (unscreened vs screened).

Temperature significantly influences relaxation mechanisms and rates.

Relaxation involves three-particle scattering processes with different dominant channels at varying energies.

Abstract

We consider the problem of relaxation in a one-dimensional system of interacting electrons. In the limit of weak interactions, we calculate the decay rate of a single-electron excitation, accounting for the nonlinear dispersion. The leading processes that determine the relaxation involve scattering of three particles. We elucidate how particular forms of Coulomb interaction, unscreened and screened, lead to different results for the decay rates and identify the dominant scattering processes responsible for relaxation of excitations of different energies. Interestingly, temperatures much smaller than the excitation energy strongly affect the rate. At higher temperatures the quasiparticle relaxes by exciting copropagating electron-hole pairs, whereas at lowest temperatures the relaxation proceeds via excitations of both copropagating and counterpropagating pairs.