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

Journal of Chemical Physics. 2018. Vol. 148. No. 2. P. 024505-1–024505-10.

Novikov S.V.

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^{1/2} 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.

Keywords: Correlated disorder model, Модель коррелированного беспорядка, diffusion coefficient, коэффициент диффузии, exponential density of states, экспоненциальная плотность состояний