Stretched exponential relaxation and ac universality in disordered dielectrics

Alexander V. Milovanov, Kristoffer Rypdal, and Jens Juul Rasmussen
Phys. Rev. B 76, 104201 – Published 4 September 2007

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.

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  • Received 30 May 2007

DOI:https://doi.org/10.1103/PhysRevB.76.104201

©2007 American Physical Society

Authors & Affiliations

Alexander V. Milovanov* and Kristoffer Rypdal

  • Department of Physics and Technology, University of Tromsø, N-9037 Tromsø, Norway

Jens Juul Rasmussen

  • Optics and Plasma Research Department, Risø National Laboratory, Technical University of Denmark, Building 128, P.O. Box 49, DK-4000 Roskilde, Denmark

  • *On leave from the Department of Space Plasma Physics, Space Research Institute, Russian Academy of Sciences,Profsoyuznaya 84/32, 117997 Moscow, Russian Federation; alexander.milovanov@phys.uit.no
  • kristoffer.rypdal@phys.uit.no
  • jens.juul.rasmussen@risoe.dk

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Issue

Vol. 76, Iss. 10 — 1 September 2007

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