Cluster Size Distribution and Relaxation Long Time Tails

Abstract

Relaxation phenomena such as the dielectric, magnetic and mechanical relaxation of many disordered physical systems exhibit universal features in particular for long time one often observes an exponential behavior known as long time tail relaxation. We show that if individual clusters in these materials have a relaxation time proportional to the cluster size, the existence of a stable probability size distribution with a long tail power law changes dramatically the relaxation rate, from an initial exponential relaxation to a long time tail t^-α. In this case it is the morphology of the system which determines its kinetics.