Microscopic model of charge carrier transfer in complex media

We present a microscopic model of a charge carrier transfer under an action of a constant electric field in a complex medium. Generalizing previous theoretical approaches, we model the dynamical environment hindering the carrier motion by dynamic percolation, i.e., as a medium comprising particles which move randomly on a simple cubic lattice, constrained by hard-core exclusion, and may spontaneously annihilate and re-appear at some prescribed rates. We determine analytically the density profiles of the “environment” particles, as seen from the stationary moving charge carrier, and calculate its terminal velocity, Vc, as the function of the applied field and other system parameters. We realize that for sufficiently small external fields the force exerted on the carrier by the “environment” particles shows a viscous-like behavior and define an analog of the Stokes formula for such dynamic percolative environments. The corresponding friction coefficient is also derived. We show that the density profile of the environment particles is strongly inhomogeneous: In front of the stationary moving charge carrier the density is higher than the average density, ρs, and approaches it as an exponential function of the distance from the carrier. Behind the carrier the local density is lower than ρs and the approach towards ρs may proceed differently depending on whether the particles number is or is not explicitly conserved.