Current flow under anomalous-diffusion conditions: Lévy walks

Abstract

We investigate the current flow under anomalous-diffusion conditions (disordered media and also turbulent motion) in the limit of strong-bias fields. A unified picture for anomalous behavior is provided by Lévy walks. These are continuous-time random walks with coupled spatial and temporal memories. We find that the long-time asymptotic behavior of the current adheres to the following power laws: dispersive transport decreasing and enhanced diffusion increasing with time. In both cases the characteristic exponents depend (in a complex way) on the memory terms. We corroborate the values of the exponents by Monte Carlo simulations.