Particle dynamics in the random barrier model: Monte Carlo simulations at low temperatures

Abstract

The low-temperature particle dynamics in the framework of the random barrier model are studied with the help of a self-developed Monte Carlo algorithm. The time-dependent mean-square displacement of the particles is, thereby, derived without using any physical approximations. Two main results are obtained. (i) In the time regime of anomalous diffusion, the mean-square displacement cannot be scaled with the diffusion coefficient of the particles. (ii) The apparent activation energy for the long-range particle transport increases slightly with temperature. These results are discussed in terms of percolation theory.