Superdiffusion in structurally disordered systems in any spatial dimension

We show that a model recently proposed by Dunlap, Kundu, and Phillips for the absence of localization in structurally disordered systems can be generalized. Specifically we show how the perfect matching condition on the diagonal and off-diagonal matrix elements can be relaxed. It is demonstrated within a tight-binding model that if the structural disorder is chosen from a bivalued distribution (that is, the nearest-neighbor potential has two minima) superdiffusion obtains even in one dimension for the majority of the site-diagonal and site-off-diagonal coupling constants characterizing real systems. In one dimension the mean-square displacement of an initially localized particle is found to grow in time as t^3/2 regardless of the magnitude of the disorder. The conditions for observing this behavior experimentally are discussed.