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

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.