Hopping models of charge transfer in a complex environment: Coupled memory continuous-time random walk approach

Charge transport processes in disordered complex media are accompanied by anomalously slow relaxation for which usually a broad distribution of relaxation times is adopted. To account for those properties of the environment, a standard kinetic approach in description of the system is addressed either in the framework of continuous-time random walks (CTRWs) or fractional diffusion. In this paper the power of the CTRW approach is illustrated by use of the probabilistic formalism and limit theorems that allow one to rigorously predict the limiting distributions of the paths traversed by charges and to derive effective relaxation properties of the entire system of interest. In particular, the standard CTRW scenario is generalized to a new class of coupled memory CTRWs that effectivly can lead to the well known Havriliak-Negami response. Application of the method is discussed for nonexponential electron-transfer processes controlled by dynamics of the surrounding medium.