Equilibration of Luttinger liquid and conductance of quantum wires

TL;DR

This paper investigates how relaxation processes in one-dimensional quantum wires cause deviations from ideal conductance quantization predicted by Luttinger liquid theory, highlighting temperature-dependent corrections influenced by wire length and excitation velocities.

Contribution

It introduces a model for relaxation effects beyond Luttinger liquid theory, quantifying their impact on conductance corrections in quantum wires.

Findings

Relaxation processes lead to conductance deviations from quantized values.

Long wires exhibit corrections based on bosonic excitation velocities.

Short wires' corrections depend on relaxation rates.

Abstract

Luttinger liquid theory describes one-dimensional electron systems in terms of non-interacting bosonic excitations. In this approximation thermal excitations are decoupled from the current flowing through a quantum wire, and the conductance is quantized. We show that relaxation processes not captured by the Luttinger liquid theory lead to equilibration of the excitations with the current and give rise to a temperature-dependent correction to the conductance. In long wires, the magnitude of the correction is expressed in terms of the velocities of bosonic excitations. In shorter wires it is controlled by the relaxation rate.