Diffusion in a one-dimensional disordered system

Abstract

The low-frequency properties of a disordered one-dimensional diffusion model are determined. Of particular interest is the case where the distribution of hopping elements diverges for small values of the hopping elements. The density of states and the leading correction terms are calculated at low frequencies and the diffusion constant and correlation length are determined. The scaling assumptions of Alexander et al. are verified. The model considered is also one for phonons with random force constants and the localization length for low-frequency phonons is determined. The case where there is both off-diagonal and diagonal disorder is considered.