Random Matrix Theory approach to Mesoscopic Fluctuations of Heat Current

TL;DR

This paper uses Random Matrix Theory to analyze mesoscopic fluctuations in heat current within large networks of oscillators, revealing universal, scale-invariant behaviors linked to strong mode correlations.

Contribution

It introduces a novel application of Random Matrix Theory to characterize universal mesoscopic fluctuations in heat transport of oscillator networks.

Findings

Average heat current is scale-invariant in large networks.

Variance of heat current also exhibits scale-invariance.

Fluctuations are indicative of strong correlations between normal modes.

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.