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

TL;DR

This paper develops a scaling theory for heat transport in disordered quasi-1D harmonic chains, revealing how heat conduction transitions from diffusive to localized regimes and providing a new framework to study Anderson localization effects.

Contribution

It introduces a novel variant of the Banded Random Matrix ensemble and demonstrates a one-parameter scaling law for phonon heat current in disordered lattices.

Findings

Heat current follows a one-parameter scaling law.

Anomalous Fourier law applies in the diffusive regime.

Heat current decays exponentially in the localization regime.

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.