relaxation time for the carrier motion in the correlated exponential DOS is unknown at the moment.

Remarks and conclusions
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We studied the transport of carriers in spatially correlated exponential DOS and found that for a wide range of correlation functions, decaying more slowly than the exponential ones, the diffusivity does not exist for temperatures well above the temperature $T_0$ of the transition to the true non-equilibrium dispersive transport regime. Breakdown of the normal diffusion is caused by the singularity of the term $\Delta D$ in . This term plays a very particular role. Indeed, for almost all correlation functions $c(x)$ $\Delta D$ serves not as a some regular contribution to the total diffusivity but as a trigger, having essentially just two values, zero and singularity. If $\Delta D=0$ then, naturally, it provides no contribution to the total $D$, and if $\Delta D$ is singular, then the normal diffusive transport does not exist and we have the case of the anomalous diffusion. The particular type of the spreading of the carriers’ packet and its possible dependence on the form of $c(x)$ will be studied in future.

Transition to the anomalous diffusion could be caused by the action of two independent 