The long time properties of diffusion in a medium with static traps

Abstract

We investigate the long time behavior of diffusion controlled absorption by randomly distributed static traps without resorting to perturbative calculations. The main idea is that the long time behavior is governed by motions in large trap‐free cavities whose probability of occurrence is small but finite. The main result is that in d dimensions, the particle density decays asymptotically slower than any exponential, according to an exp[−t^d/(d+2)] behavior. This and other predictions are verified with numerical simulations.