Diffusion with random distribution of static traps
Abstract
The random walk problem is studied in two and three dimensions in the presence of a random distribution of static traps. An efficient Monte Carlo method, based on a mapping onto a polymer model, is used to measure the survival probability P(c,t) as a function of the trap concentration c and the time t. Theoretical arguments are presented, based on earlier work of Donsker and Varadhan and of Rosenstock, why in two dimensions one expects a data collapse if -ln[P(c,t)]/ln(t) is plotted as a function of (lambda t)^{1/2}/ln(t) (with lambda=-ln(1-c)), whereas in three dimensions one expects a data collapse if -t^{-1/3}ln[P(c,t)] is plotted as a function of t^{2/3}lambda. These arguments are supported by the Monte Carlo results. Both data collapses show a clear crossover from the early-time Rosenstock behavior to Donsker-Varadhan behavior at long times.
Cite
@article{arxiv.cond-mat/0105163,
title = {Diffusion with random distribution of static traps},
author = {G. T. Barkema and Parthapratim Biswas and Henk van Beijeren},
journal= {arXiv preprint arXiv:cond-mat/0105163},
year = {2009}
}
Comments
4 pages, 6 figures