Time transformation for random walks in the quenched trap model

S. Burov, E. Barkai

Published 2010-12-28Version 1

Diffusion in the quenched trap model is investigated with an approach we call weak subordination breaking. We map the problem onto Brownian motion and show that the operational time is ${\cal S}_\alpha = \sum_{x=-\infty} ^\infty (n_x)^\alpha$ where $n_x$ is the visitation number at site $x$ . In the limit of zero temperature we recover the renormalization group (RG) solution found by Monthus. Our approach is an alternative to RG capable of dealing with any disorder strength.