Role of pinning potentials in heat transport through disordered harmonic chains

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)similar to 1/N-1/2 while in the presence of one or two pins < J >(Fi)similar to 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)similar to 1/Nn-1/2. We discuss the relevance of our results in the context of recent experiments.