Stochastic transport and relaxation in disordered systems: CTRW-models and simulation calculations

Many excitation relaxation phenomena in ordered and disordered systems can be modelled by diffusion controlled pseudounimolecular A+B→B and bimolecular A+A→0 reactions. Here only a few exact results are known and one has, in general, to apply approximate forms. Both for the phenomenological investigation of such exciton processes and for assessing the quality of approximations computer simulations have proved to be useful. In this work we focus on the continuous-time random-walk method (CTRW). A central role in the description of reactions is played by S(t), the mean number of distinct sites visited in time t. We exemplify our procedures using Lévy walks i.e. systems with coupled spatio-temporal memories. For Lévy walks S(t) shows as a function of the memory-parameters a very interesting, non-universal, non-monotonic behavior. We compare the findings with those for decoupled CTRWs on regular lattices.