Renormalization group approach to random walks on disordered lattices

Abstract

One-dimensional random walks with static disorder are analyzed using a real space renormalization group procedure. The presence of disorder leads to a non-Markovian description of the macroscopic behavior of the random walk. We consider random walks with nearest-neighbor hopping described by a master equation with both on-site and site-to-site disorder in the transition matrix. Site-to-site disorder leads to a generalized diffusion coefficient with at−3/2 long time tail whereas on-site disorder leads to a generalized Burnett coefficient with at−1/2 long time tail.