# Thermal conductance of one dimensional disordered harmonic chains

## TL;DR

This paper investigates how disorder affects heat conduction in one-dimensional harmonic chains, revealing universal scaling laws and conditions under which Fourier's law is satisfied.

## Contribution

It introduces a universal scaling parameter linking disorder, temperature, and localization length, providing new insights into phonon-mediated heat conduction in disordered systems.

## Key findings

- Thermal conductance scales non-trivially with system size.
- Strong disorder with heavy-tailed distributions can satisfy Fourier's law.
- A universal behavior of conductance emerges when considering the scaling parameter.

## Abstract

We study heat conduction mediated by longitudinal phonons in one dimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find non-trivial scaling of the thermal conductance with the system size. Our findings are corroborated by extensive numerical analysis. We show that a system with strong disorder, characterized by a `heavy-tailed' probability distribution, and with large impedance mismatch between the bath and the system satisfies Fourier's law. We identify a dimensionless scaling parameter, related to the temperature scale and the localization length of the phonons, through which the thermal conductance for different models of disorder and different temperatures follows a universal behavior.