Relaxation processes in a disordered Luttinger liquid

TL;DR

This paper investigates relaxation processes in a disordered Luttinger liquid, revealing that energy equilibration rates are primarily determined by elastic scattering off disorder, independent of interactions and temperature.

Contribution

It introduces a kinetic framework for analyzing nonequilibrium dynamics in disordered Luttinger liquids, highlighting the dominant role of elastic scattering in energy relaxation.

Findings

Energy equilibration rate equals elastic scattering rate at high temperature.

Relaxation processes differ from electron-electron scattering and phase relaxation.

Disorder-induced localization effects are suppressed by dephasing at high temperatures.

Abstract

The Luttinger liquid model, which describes interacting electrons in a single-channel quantum wire, is completely integrable in the absence of disorder and as such does not exhibit any relaxation to equilibrium. We consider relaxation processes induced by inelastic electron-electron interactions in a disordered Luttinger liquid, focusing on the equilibration rate and its essential differences from the electron-electron scattering rate as well as the rate of phase relaxation. In the first part of the paper, we review the basic concepts in the disordered Luttinger liquid at equilibrium. These include the elastic renormalization, dephasing, and interference-induced localization. In the second part, we formulate a conceptually important framework for systematically studying the nonequilibrium properties of the strongly correlated (non-Fermi) Luttinger liquid. We derive a coupled set of kinetic equations for the fermionic and bosonic distribution functions that describe the evolution of the nonequilibrium Luttinger liquid. Remarkably, the energy equilibration rate in the conducting disordered quantum wire (at sufficiently high temperature, when the localization effects are suppressed by dephasing) is shown to be of the order of the rate of elastic scattering off disorder, independent of the interaction constant and temperature.