Time-dependent diffusion in a random correlated potential

Diffusive behavior of a particle in a two-dimensional random correlated potential with Gaussian distribution and exponential correlation is investigated via Langevin simulation. Our results show that superdiffusion appears only in the early period of the time of evolution and there does not exist an intermediate time for the occurrence of the whole issue from subdiffusion to superdiffusion. Whether the asymptotic situation of the particle could be arrived before the simulation stops is strongly influenced by the finite-size effect of the random correlated potential simulated. By applying the random correlated potential to the decay of a metastable system, we find that the escape rate of a particle is decreased by hill effect of the random potential.