the non-equilibrium dispersive transport regime, while for $kT/U_0 > 1$ a quasi-equilibrium regime with constant velocity $v$ eventually develops [@Rudenko:177; @Arkhipov:189]. There is a general agreement that for the high temperature $kT/U_0 > 1$ the long time behavior is accurately described by the normal diffusive transport.

Nonetheless, in all previous studies a very important ingredient of the random energy energy landscape has been omitted, namely the possible spatial correlation of random energies. Recently we considered the behavior of the average particle velocity $v$ for the spatially correlated exponential DOS and its dependence on temperature and driving force strength [@Novikov:24504]. Exact analytic solution has been obtained for the quasi-equilibrium nondispersive regime $kT/U_0 > 1$ and an approximate approach has been suggested for the dispersive regime $kT/U_0 < 1$. Here we are going to extend our consideration to the calculation of the diffusivity $D$, exclusively concentrating our attention on the nondispersive case. It turns out that this case is not so trivial for the spatially correlated energy landscape.

For the sake of simplicity we use the exact exponential DOS with sharp cut-off at $U=0$ $$\label{exp-DOS1}
g(U)=\frac{N_0}{U_0}e^{U/U_0},\hskip10pt U < 0,$$ where $N_0$ is the total concentration of hopping sites and $g(U)=0$ for $U 