> 0$. We mostly consider the temperature being close to $U_0/k$, where particle spends almost all time in the deep states $U\ll -U_0$. For this reason the exact form of the DOS for $U > 0$ is not important. More thorough discussion may be found in Ref. .

For the 1D case Parris et al. derived a general formula for the diffusivity of the charged particle moving in the arbitrary potential $U(x)$ which is periodic with the period $L$ [@Parris:5295; @Parris:2803]. In the limit $L\rightarrow\infty$ this formula provides the possibility to obtain the relation for the diffusivity statistically averaged over realizations of $U(x)$ $$\begin{aligned}
\label{D}
&D=D_0\frac{\partial v}{\partial v_0}+\Delta D,\hskip10pt v=\frac{D_0}{\int\limits_0^\infty dx e^{-\gamma x}Z_2(x)},\\
\label{rr}
&\Delta D=\frac{v^3}{D_0^2}\int\limits_0^\infty dy dz e^{-\gamma(y+z)}G(y,z),\hskip10pt \gamma=v_0/D_0,\\
\label{lin}
&G(y,z)=\lim\limits_{L\rightarrow\infty}\frac{1}{L}\int\limits_0^L dx x \left[Z_4(x,y,z)-Z_2(y)Z_2(z)\right],\\
\label{z2z4}
&Z_2(x)=\left<e^{\left[U(x)-U(0)\right]/kT}\right>,\hskip10pt
Z_4(x,y,z)=\left<e^{\left[U(x+y)-U(x)+U(0)-U(-z)\right/kT}\right>,\end{aligned}$$ here the angular brackets mean the average over realization of $U(x)$, $\mu_0$ and $v_0=\mu_0 E$ are the carrier mobility and velocity for the system without disorder. Hence, the task to calculate the diffusivity is essentially shifted to the calculation of the correlation functions $Z_2(x)$ and $Z_4(x,y,z)$. If the second term in is zero, then this equation is, in fact, the modified Einstein relation (mER) [@Parris:5295; @Parris:2803], albeit written using the carrier velocity 