# Resistor-network anomalies in the heat transport of random harmonic chains Academic Article

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### 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 $G\ensuremath{\propto}1/{L}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}=1$ 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.

### publication date

• January 1, 2016