Stretched exponential relaxation arising from a continuous sum of exponential decays

By D. Johnston. 2006

366 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cfdd8c189c899f438441ac81dc0506780893ee60

How researchers see this paper

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In Atomic and Molecular Physics, and Optics

1. C. Kochanek
2. M. Oguri
3. Dominique Sluse
4. Leon V. E. Koopmans
5. P. Schneider

In Statistical and Nonlinear Physics

1. Y. Zu
2. C. Kochanek
3. M. Bartelmann

Citations in the corpus

• IS QUASAR OPTICAL VARIABILITY A DAMPED RANDOM WALK? (2012, background): “The combination of P (s, γ)σ2(sτ) is then the inverse Laplace transform of the powered exponential (Johnston 2006).”