Heat transport in disordered quantum harmonic oscillator chains

TL;DR

This paper investigates heat conduction in disordered quantum harmonic chains connected to reservoirs, deriving exact expressions for thermal current and analyzing size dependence, revealing classical-like power law behavior influenced by reservoir spectra.

Contribution

It provides formal exact formulas for quantum heat transport in disordered chains and explores their size dependence, linking quantum results to classical behavior.

Findings

Thermal current expressions reduce to Landauer-like forms in special cases

Heat current exhibits power law dependence on system size

Dependence on spectral properties of reservoirs

Abstract

We study heat conduction in quantum disordered harmonic chains connected to general heat reservoirs which are modeled as infinite collection of oscillators. Formal exact expressions for the thermal current are obtained and it is shown that, in some special cases, they reduce to Landauer-like forms. The asymptotic system size dependence of the current is analysed and is found to be similar to the classical case. It is a power law dependence and the power depends on the spectral properties of the reservoirs.