Anomalous diffusion in disordered multi-channel systems

Abstract

We study diffusion of a particle in a system composed ofK parallel channels, where the transition rates within the channels arequenched random variables whereas the inter-channel transition ratev is homogeneous. A variant of the strong disorder renormalization groupmethod and Monte Carlo simulations are used. Generally, we observeanomalous diffusion, where the average distance traveled by the particle,[⟨x(t)⟩]av, has a power-law timedependence [⟨x(t)⟩]av ∼ tμK(v), witha diffusion exponent 0 ≤ μK(v) ≤ 1. In the presence of left–right symmetry of the distribution of randomrates the recurrent point of the multi-channel system is independent ofK and the diffusion exponent is found to increase withK and decreasewith v. In the absence of this symmetry, the recurrent point may be shifted withK and the current can be reversed by varying the lane change ratev.