Role of pinning potentials in heat transport through disordered harmonic chains

Abstract

The role of quadratic on-site pinning potentials on determining the size (N) dependence of the disorder averaged steady state heat current <J> in an 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>_Fr~1/N^½ while in the presence of one or two pins <J>_Fi~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>_n~1/N^n-½. We discuss the relevance of our results in the context of recent experiments.