Origin of Stretched Exponential Relaxation for Hopping-Transport Models

We propose a novel geometric approach to the description of the relaxation phenomena in complex condensed-matter systems. It is shown within a fairly general random site hopping model that the stretched exponential decay law, exp([-(t/tau)(beta)], originates from the simple and general geometric features of a random distribution of transport and trapping sites in the 3D space. The value of the variable stretching index beta is determined by the localization radius of hopping electrons. The possibilities for generalization of the obtained results and interpretation of the relevant experimental data are discussed.