Stretched exponential relaxation and ac universality in disordered dielectrics

Alexander V. Milovanov; Jens Juul Rasmussen; Kristoffer Rypdal

doi:10.1103/physrevb.76.104201

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arXiv · 0705.4417

Stretched exponential relaxation and ac universality in disordered dielectrics

Alexander V. Milovanov·Jens Juul Rasmussen·Kristoffer Rypdal

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Abstract

This paper is concerned with the connection between the properties of dielectric relaxation and ac (alternating-current) conduction in disordered dielectrics. The discussion is divided between the classical linear-response theory and a self-consistent dynamical modeling. The key issues are, stretched exponential character of dielectric relaxation, power-law power spectral density, and anomalous dependence of ac conduction coefficient on frequency. We propose a self-consistent model of dielectric relaxation, in which the relaxations are described by a stretched exponential decay function. Mathematically, our study refers to the expanding area of fractional calculus and we propose a systematic derivation of the fractional relaxation and fractional diffusion equations from the property of ac universality.

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Alexander V. Milovanov, Jens Juul Rasmussen, Kristoffer Rypdal. 2007-05-30. Stretched exponential relaxation and ac universality in disordered dielectrics. https://doi.org/10.1103/physrevb.76.104201

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