Nonequilibrium kinetics of a disordered Luttinger liquid

TL;DR

This paper develops a kinetic theory for disordered Luttinger liquids out of equilibrium, revealing that the equilibration rate equals the elastic backscattering rate and is unaffected by interaction strength, temperature, or bias.

Contribution

It introduces a kinetic framework for disordered Luttinger liquids and shows that the equilibration rate is determined by elastic backscattering, independent of interaction parameters.

Findings

Equilibration rate equals elastic backscattering rate.

No relaxation to equilibrium in the absence of inhomogeneities.

Rate is independent of interaction strength, temperature, and bias.

Abstract

We develop a kinetic theory for strongly correlated disordered one-dimensional electron systems out of equilibrium, within the Luttinger liquid model. In the absence of inhomogeneities, the model exhibits no relaxation to equilibrium. We derive kinetic equations for electron and plasmon distribution functions in the presence of impurities and calculate the equilibration rate $\gamma_E$. Remarkably, for not too low temperature and bias voltage, $\gamma_E$ is given by the elastic backscattering rate, independent of the strength of electron-electron interaction, temperature, and bias.