Anomalous transport properties for random-hopping and random-trapping models

Abstract

Previous work on anomalous transport is extended to two and three dimensions. Using critical-path analysis it is shown that random-hopping models always lead to a finite dc conductivity and diffusion constant and thus to normal asymptotic behavior above 1D. For RT models anomalous behavior is shown to be possible with indices in agreement with the Scher-Lax theory, above 2D. It is also pointed out that such behavior is to be expected for an exponential tail of traps and the temperature dependence is predicted.