On electronic energy transfer in disordered systems

A generalized master equation (GME) describing the incoherent motion of an excitation in a disordered system is developed. The connection of the GME to the semi-Markovian theory of Scher and Lax, the generalized continuous random walk, and the self-energy approaches to the temporal properties of the transport is discussed. The theory is used in a model calculation to compute the mean square displacement and the probability of the excitation to remain at the origin as functions of time, and the results are compared to recent work on one dimensional systems, in which only nearest neighbor interactions are included.