Stretched Exponential Relaxation Arising from a Continuous Sum of Exponential Decays
Abstract
Stretched exponential relaxation of a quantity n versus time t according to n = n_0 exp[-(lambda* t)^beta] is ubiquitous in many research fields, where lambda* is a characteristic relaxation rate and the stretching exponent beta is in the range 0 < beta < 1. Here we consider systems in which the stretched exponential relaxation arises from the global relaxation of a system containing independently exponentially relaxing species with a probability distribution P(lambda/lambda*,beta) of relaxation rates lambda. We study the properties of P(lambda/lambda*,beta) and their dependence on beta. Physical interpretations of lambda* and beta, derived from consideration of P(lambda/lambda*,beta) and its moments, are discussed.
Keywords
Cite
@article{arxiv.cond-mat/0609331,
title = {Stretched Exponential Relaxation Arising from a Continuous Sum of Exponential Decays},
author = {D. C. Johnston},
journal= {arXiv preprint arXiv:cond-mat/0609331},
year = {2010}
}
Comments
8 pages, 10 figures; version to be published in Phys. Rev. B