Nonlinear field dependence of the mobility of a charge subjected to a superposition of dichotomous stochastic potentials

A general prescription is presented to address a large variety of forms of the nonlinear dependence of the static charge mobility on the applied electric field.:The system consists of a classical charge subjected to an arbitrarily strong steady state electric field and to a stochastic potential consisting of a linear superposition of an unlimited number of dichotomous potentials in one-dimensional space. It is shown that the nonlinear mobility can be calculated for arbitrary forms of the density function of the individual dichotomous components of the stochastic potential. Specific cases of physical interest are analyzed. One of them provides a curious possibility for an explanation of the Universally observed square root field dependence of the logarithm of the mobility of photoinjected charge carriers in molecularly doped polymers.