Diffusion of a particle in the spatially correlated exponential random energy landscape: transition from normal to anomalous diffusion

摘要

Diffusive transport of a particle in spatially correlated random energylandscape having exponential density of states has been considered. We exactlycalculate the diffusivity in the nondispersive quasi-equilibrium transportregime and found that for slow decaying correlation functions the diffusivitybecomes singular at some particular temperature higher than the temperature ofthe transition to the true non-equilibrium dispersive transport regime. Itmeans that the diffusion becomes anomalous and does not follow the usual$\propto t^{1/2}$ law. In such situation the fully developed non-equilibriumregime emerges in two stages: first, at some temperature there is thetransition from the normal to anomalous diffusion, and then at lowertemperature the average velocity for the infinite medium goes to zero, thusindicating the development of the true dispersive regime. Validity of theEinstein relation is discussed for the situation where the diffusivity doesexist.