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

Abstract

Diffusive transport of a particle in a spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime for the 1D transport model and found that for slow decaying correlation functions the diffusivity becomes singular at some particular temperature higher than the temperature of the transition to the true non-equilibrium dispersive transport regime. It means that the diffusion becomes anomalous and does not follow the usual ∝ t law. In such situation, the fully developed non-equilibrium regime emerges in two stages: first, at some temperature there is the transition from the normal to anomalous diffusion, and then at lower temperature the average velocity for the infinite medium goes to zero, thus indicating the development of the true dispersive regime. Validity of the Einstein relation is discussed for the situation where the diffusivity does exist. We provide also some arguments in favor of conservation of the major features of the new transition scenario in higher dimensions.

Charge transport in the spatially correlated exponential random energy landscape: effect of the nonpositive correlation function

“…Recently the behavior of the average carrier velocity v and diffusivity D for the hopping transport in the disordered medium having spatially correlated eDOS has been studied for the continuous model of charge transport. 24,25 The average particle velocity in the infinite transport medium iswhere angular brackets mean statistical averaging over realization of U ( x ). 26–28…”

“…It was found that spatial correlation significantly changes transport properties, determines the dependence of the mobility on v 0 , and provides unusual transport properties (breakdown of the normal diffusion) in the case of the long range correlations. 24,25 If Z ( x ) → ∞, then v goes to 0, thus signalling the transition to the dispersive transport regime where the average carrier velocity depends on the thickness L of the transport layer. Divergence of Z ( x ) takes place when1 − κ 2 [1 − c 2 ( x )] → 0and the true critical value κ c is defined by the minimal value of c 2 ( x ), i.e.…”