ANOMALOUS RELAXATION IN THE FRACTAL TIME RANDOM-WALK MODEL

We study relaxation properties of the fractal time random walk model in which the waiting time distribution is given by the power law type t-1-a. By means of theoretical analyses as well as of Monte Carlo simulations of this model, we find that the relaxation becomes anomalous in the case of a<1 where the complex susceptibility is described by the Cole-Cole form. On the other hand, the normal Debye type relaxation is observed for a>1. We also find the scaling laws both for the relaxation function and for the particle density. © 1995 The American Physical Society.