On the probability distributions of relaxation times in glasses*
Institut für Physik, Universität Dortmund, 44221
Corresponding author: a firstname.lastname@example.org
Accepted: 17 March 1998
Published online: 15 October 1998
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.
PACS: 02.30.Rz – Integral equations / 77.22.Ch – Permittivity (dielectric function) / 81.05.Kf – Glasses (including metallic glasses)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998