Eur. Phys. J. B 5, 599-603 (1998)
https://doi.org/10.1007/s100510050484

On the probability distributions of relaxation times in glasses^*

Institut für Physik, Universität Dortmund, 44221 Dortmund, Germany

Corresponding author: ^a keiter@fkt.physik.uni-dortmund.de

Received: 2 February 1998
Accepted: 17 March 1998
Published online: 15 October 1998

Abstract

The scale of relaxation times in glasses has led to generalizations of the Drude model of the dielectric function in terms of an integral, containing a Drude kernel and a probability distribution. This integral equation is solved by a Mellin or a Stieltjes transform. Beyond known results, we obtain the probability distribution of the Havriliak-Negami dielectric function. Even more general classes of dielectric models can be dealt with, using Mellin's transform. They may serve as checks for numerical procedures applied to the underlying ill-posed problem, if experimental data for the dielectric function are used.