Generalized diffusion coefficient in one-dimensional random walks with static disorder

Abstract

A real-space renormalization-group method is applied to one-dimensional random walks with static disorder. In agreement with previous results we find that the presence of disorder leads to a non-Markovian diffusion equation with a $t^{-\frac{3}{2}}$ long-time tail. The effective diffusion coefficient and the coefficient of the long-time tail are computed for several disordered random walks.