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 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