Scaling Theory of Heat Transport in Quasi-1D Disordered Harmonic Chains

Abstract

We introduce a variant of the Banded Random Matrix ensemble and show, using detailed numerical analysis and theoretical arguments, that the phonon heat current in disordered quasi-one-dimensional lattices obeys a one-parameter scaling law. The resulting beta-function indicates that an anomalous Fourier law is applicable in the diffusive regime, while in the localization regime the heat current decays exponentially with the sample size. Our approach opens a new way to investigate the effects of Anderson localization in heat conduction, based on the powerful ideas of scaling theory.

arXiv commentSupplemental Report on calculation of heat current included

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• Enhancement and reduction of one-dimensional heat conduction with correlated mass disorder
• Thermal conductance of one dimensional disordered harmonic chains
• Thermal conductivity in 1d: disorder-induced transition from anomalous to normal scaling
• Random Matrix Theory approach to Mesoscopic Fluctuations of Heat Current
• Ballistic Heat Conduction and Mass Disorder in One Dimension
• Eliminating the cuspidal temperature profile of a non-equilibrium chain
• Resistor-network anomalies in the heat transport of random harmonic chain