Resistor-network anomalies in the heat transport of random harmonic chain

TL;DR

This paper investigates how disorder affects heat conduction in low-dimensional harmonic networks, revealing anomalies in thermal conductance scaling related to Anderson localization and glassy disorder.

Contribution

It derives the dependence of thermal conductance on system length in disordered harmonic chains, highlighting anomalies due to glassy disorder and duality with Lifshitz-tail regimes.

Findings

Thermal conductance G scales with length L following a non-Fourier law.

Glassy disorder induces anomalies linked to Anderson localization.

Duality relates these anomalies to Lifshitz-tail regimes in Anderson models.

Abstract

We consider thermal transport in low-dimensional disordered harmonic networks of coupled masses. Utilizing known results regarding Anderson localization, we derive the actual dependence of the thermal conductance $G$ on the length $L$ of the sample. This is required by nanotechnology implementations because for such networks Fourier's law $G \propto 1/L^{\alpha}$ with $\alpha=1$ is violated. In particular we consider "glassy" disorder in the coupling constants, and find an anomaly which is related by duality to the Lifshitz-tail regime in the standard Anderson model.