Dynamical model for stretched exponential relaxation in solids

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Abstract
A dynamical model for stretched exponential relaxation in solids is developed. The essential assumption is that the relaxation of a macroscopic parameter can take place simultaneously via a large number of channels, each of which is controlled by a thermally activated ‘‘gate’’ that opens and closes at random with transition rates that satisfy detailed balancing conditions. It is further assumed that the probability of any individual channel being open is vanishingly small, although the spectral density of open channels is finite. It is shown that in the model, stretched exponential relaxation reflects scaling behavior in the joint distribution of relaxation rates and transition rates for the open channels. The behavior is similar to an analogous static model treated previously and reduces to that of the static model when the transition rates for the gates approach zero. © 1996 The American Physical Society.