Stretched Exponential Relaxation Arising from a Continuous Sum of Exponential Decays

Details Stretched Exponential Relaxation Arising from a Continuous Sum of Exponential Decays Stretched Exponential Relaxation Arising from a Continuous Sum of Exponential Decays

2006-09-13

arxiv.org/abs/cond-mat/0609331v2

Phys. Rev. B 74, 184430 (2006); 7 pages. Erratum 77, 179901(E) (2008); 1 page

Physics

Condensed Matter

Statistical Mechanics

8 pages, 10 figures; version to be published in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.74.184430

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.

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