Role of pinning potentials in heat transport through disordered harmonic chain

TL;DR

This paper investigates how onsite pinning potentials affect the size dependence of heat current in disordered harmonic chains, revealing that pinning centers significantly alter heat transport scaling.

Contribution

It provides a comprehensive analysis of the impact of pinning potentials on heat current scaling in disordered chains, supported by heuristic arguments and numerical evidence.

Findings

Without pinning, <J> ~ 1/N^{1/2}

With n pinning centers, <J> ~ 1/N^{n-1/2}

Results are relevant for interpreting recent heat transport experiments

Abstract

The role of quadratic onsite pinning potentials on determining the size (N) dependence of the disorder averaged steady state heat current <J>, in a isotopically disordered harmonic chain connected to stochastic heat baths, is investigated. For two models of heat baths, namely white noise baths and Rubin's model of baths, we find that the N dependence of <J> is the same and depends on the number of pinning centers present in the chain. In the absence of pinning, <J> ~ 1/N^{1/2} while in presence of one or two pins <J> ~ 1/N^{3/2}. For a finite (n) number of pinning centers with 2 <= n << N, we provide heuristic arguments and numerical evidence to show that <J> ~ 1/N^{n-1/2}. We discuss the relevance of our results in the context of recent experiments.