Interaction effects on thermal transport in quantum wires

TL;DR

This paper develops a theory for thermal transport in quantum wires with weak electron interactions, highlighting the role of three-particle collisions in energy relaxation and deriving an expression for thermal conductance.

Contribution

It introduces an analytic model for thermal conductance in quantum wires considering three-particle collisions and partial equilibration, valid across different wire lengths.

Findings

Thermal conductance correction saturates in long wires.

Intrabranch scattering establishes partial equilibrium.

Interbranch processes govern energy exchange.

Abstract

We develop a theory of thermal transport of weakly interacting electrons in quantum wires. Unlike higher-dimensional systems, a one-dimensional electron gas requires three-particle collisions for energy relaxation. The fastest relaxation is provided by the intrabranch scattering of comoving electrons which establishes a partially equilibrated form of the distribution function. The thermal conductance is governed by the slower interbranch processes which enable energy exchange between counterpropagating particles. We derive an analytic expression for the thermal conductance of interacting electrons valid for arbitrary relation between the wire length and electron thermalization length. We find that in sufficiently long wires the interaction-induced correction to the thermal conductance saturates to an interaction-independent value.