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.Comment: 8 pages, 2 figure
