Direct Numerical Observation of Anomalous Diffusion in Random Media

Abstract

We present computer simulations of anomalous diffusion, $< r^2(t) > \sim a t^{1-δ}$, in two dimensions. The Monte Carlo calculations are in excellent agreement with previous renormalization group calculations. Interestingly, use of a high quality pseudo-random number generator is necessary to observe the anomalous diffusion. A linear-feedback, shift-register method leads to incorrect, ballistic motion of the random walkers.