Hopping Models of Charge Transfer in a Complex Environment: New Class of Coupled Memory Continous-Time Random Walks

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 (CTRW) 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 to predict the limiting distributions of the paths traversed by charges and to derive effective relaxation properties of the entire system of interest. Application of the method is discussed for non-exponential electron-transfer processes controlled by dynamics of the surrounding medium.