Origin of Stretched Exponential Relaxation for Hopping-Transport Models

Abstract

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.