$v_0$ instead of the applied electric field $E$. The simple Einstein relation $$D=\frac{kT}{e}\mu
\label{sER}$$ is not valid in the materials having field-dependent carrier mobility $\mu$, apart from the limit case $E=0$. We will consider the applicability of the mER for the exponential spatially correlated DOS.

Correlation functions $Z_2(x)$ and $Z_4(x,y,z)$ diverge for low temperature $kT < U_0$ (dispersive transport regime). This can be immediately seen when all coordinates of $Z_2(x)$ and $Z_4(x,y,z)$ go to infinity, because all exponentials in become independent and, for example, $$Z_2(x\rightarrow\infty)\rightarrow \left<e^{U(x)/kT}\right>\left<e^{-U(0)/kT}\right>=
\frac{1}{1-\varkappa^2},\hskip10pt \varkappa=U_0/kT.
\label{z2inf}$$ Correlation function $Z_4(x,y,z)$ has a similar singularity at $\varkappa\rightarrow 1$. This divergence indicates the invalidity of Eqs. (\[D\]-\[z2z4\]) connected with the transition to the non-equilibrium dispersive transport regime at $\varkappa > 1$ where the average velocity goes to 0 for the infinite medium. The difficulty to carry out the calculations for the dispersive regime is directly connected with the necessity to consider transport for a transport layer having the finite thickness. Possibility to consider quasi-equilibrium transport in the infinite medium greatly facilitates the calculations.

It is easy to see that the divergence at $\varkappa\rightarrow 1$ is the only singularity of $Z_2(x)$ and $Z_4(x,y,z)$ for the case of spatially uncorrelated disorder where 