Thermal transport in disordered harmonic chains revisited: Formulation of thermal conductivity and local temperatures

TL;DR

This paper investigates thermal transport in disordered harmonic chains using nonequilibrium Green's functions, revealing size-independent conductivity at strong disorder and deriving a universal temperature profile formula.

Contribution

It provides a unified framework linking localization length to thermal conductivity and local temperature profiles in disordered harmonic chains.

Findings

Thermal conductivity becomes size-independent at strong disorder.

Local temperatures exhibit nonlinear profiles, deviating from Fourier's law.

Self-consistent reservoirs restore linear temperature profiles even at weak coupling.

Abstract

In this paper, thermal transport in bond-disordered harmonic chains is revisited in detail using a nonequilibrium Green's function formalism. For strong bond disorder, thermal conductivity is independent of the system size. However, kinetic temperatures described by the local number of states coupling to external heat reservoirs are anomalous since they form a nonlinear profile in the interior of the system. Both results are accounted for in a unified manner in terms of the frequency-dependent localization length. From this argument, we derive a generic formula describing the asymptotic profile of local temperatures in a disordered harmonic chain. A linear temperature profile obeying Fourier's law is recovered by contact with a self-consistent reservoir of Ohmic type even in the limit of weak system-reservoir coupling. This verifies that mechanisms leading to local thermal equilibrium and breaking total momentum conservation are essential for Fourier transport in low dimensions.