Energy transfer as a continuous time random walk

Abstract

In this work we study the energy migration on regular lattices in the framework of a continuous time random walk (CTRW). This extends our former investigations [A. Blumen and G. Zumofen, J. Chem. Phys. 75, 892 (1981); G. Zumofen and A. Blumen, J. Chem. Phys. 76, 3713 (1982)] to the continuous time domain. Here the ingredient is the stepping time distribution function ψ(t). We derive this function from an exact formalism, for microscopic transfer rates due to multipolar and to exchange interactions. Furthermore, we study the decay law due to trapping by randomly distributed substitutional traps, starting from an exact expression. We analyze the interplay between the temporal and the pure random‐walk stochastic aspects, and their respective influence on the decay law. The analysis is rendered transparent by using the cumulants of the random variables, which also offers a means to derive handy approximate expressions for the decay laws. We exemplify the findings for a square and a simple cubic lattice for CTRW mediated by dipolar interactions, as compared to random walks with constant stepping frequency.