Effect of motion of the scatterers on localization: Quasi localization and quasi mobility edge

We study kinetics of electrons, scattered by heavy particles undergoing slow diffusive motion. In a three-dimensional space we claim the existence of the crossover region (on the energy axis), which separates the states with fast diffusion and the states with slow diffusion; the latter is determined by the dephasing time. In a two-dimensional space the diffusion coefficient for any value of energy is determined by the dephasing time. We discuss relevance of the results obtained for the propagation of light in a disordered medium.