Localization and Spectral Singularities in Random Chains

Abstract

This paper reports consideration of the Hamiltonian for tight binding in one dimension with off-diagonal disorder of two forms, corresponding to Dyson's types I and II. The density of states and localization function at the center of the band are found by perturbation theory and a scaling argument. The distinction between the two types of disorder is clearly drawn, and new singularities in the Green's function pertinent to the problem of random classical diffusion are predicted.