Stretched exponential relaxation and ac universality in disordered dielectrics

TL;DR

This paper explores the relationship between dielectric relaxation and ac conduction in disordered dielectrics, proposing a self-consistent model based on fractional calculus to explain stretched exponential relaxation and ac universality.

Contribution

It introduces a self-consistent dynamical model linking dielectric relaxation with ac conduction using fractional calculus, advancing understanding of disordered dielectric behavior.

Findings

Dielectric relaxation follows a stretched exponential decay.

The model explains power-law spectral density and ac conduction dependence.

Fractional relaxation and diffusion equations are derived from ac universality.

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.