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

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.