Stretched exponential relaxation and ac universality in disordered dielectrics

Details Stretched exponential relaxation and ac universality in disordered dielectrics Stretched exponential relaxation and ac universality in disordered dielectrics

2007-05-30

arxiv.org/abs/0705.4417v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages, 2 figures

Scientific paper

10.1103/PhysRevB.76.104201

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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