Stretched exponential relaxation and ac universality in disordered dielectrics

Alexander V. Milovanov, Kristoffer Rypdal, Jens Juul Rasmussen

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    Abstract

    This paper is concerned with the connection between the properties of dielectric relaxation and alternating-current (ac) 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.
    Original languageEnglish
    JournalPhysical Review B Condensed Matter
    Volume76
    Issue number10
    Pages (from-to)104201
    ISSN0163-1829
    DOIs
    Publication statusPublished - 2007

    Bibliographical note

    Copyright 2007 American Physical Society

    Keywords

    • CHAOS
    • FRACTIONAL KINETICS
    • DIFFUSION
    • EMPIRICAL DECAY FUNCTION
    • ANOMALOUS TRANSPORT
    • BEHAVIOUR
    • DYNAMICS

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