KINETIC NETWORKS AND ORDER-STATISTICS FOR HOPPING IN DISORDERED-SYSTEMS

A critical comparison between geometrical networks (based on some bonding criterion) and kinetic networks (the actual path of the carrier) is made for dispersive hopping in disordered systems. The method of order statistics is used for the characterization of the kinetic network. These statistics describe the distributions of first, second and higher transition rates out of a given site to other sites in a hopping configuration and can adequately explain the structure of the kinetic network for the strong disorder case, via consideration of chain growth versus branching. Using numerical simulation a detailed investigation of how the structure of the kinetic network changes with increasing disorder is presented. When disorder is strong, the kinetic network becomes predominantly one-dimensional and is actually a small subset of the geometrical network. As one of the consequences, the kinetics due to capture at recombination centres slow down and become close to behaviour typical for one dimension.