Thermal transport in phononic Cayley-tree networks

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

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∝1/L^{α} with α=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.