Random Matrix Theory approach to Mesoscopic Fluctuations of Heat Current

Abstract

We consider an ensemble of fully connected networks of N oscillators coupled harmonically with random springs and show, using Random Matrix Theory considerations, that both the average phonon heat current and its variance are scale-invariant and take universal values in the large N-limit. These anomalous mesoscopic uctuations is the hallmark of strong correlations between normal modes.

6 pages,3 figures

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• Non-equilibrium steady states of long-range coupled harmonic chains
• Dynamics of Disordered Mechanical Systems with Large Connectivity, Free Probability Theory, and Quasi-Hermitian Random Matrices
• Thermal Transport in Phononic Cayley Tree Networks
• Resistor-network anomalies in the heat transport of random harmonic chain