# H-function representations for stretched exponential relaxation
and Non-Debye susceptibilities in glassy systems

R. Hilfer

ICA-1, Universität Stuttgart, Pfaffenwaldring 27, 70569 Stuttgart

Institut für Physik, Universität Mainz, 55099 Mainz, Germany

###### Abstract.

Analytical expressions in the time and frequency
domains are derived for non-Debye relaxation processes.
The complex frequency dependent
susceptibility function for the stretched exponential
relaxation function is given for
general values of the stretching exponent
in terms of H-functions.
The relaxation functions corresponding to the
complex frequency dependent Cole-Cole,
Cole-Davidson and Havriliak-Negami
susceptibilities are given in
the time domain in terms of H-functions.
It is found that a commonly used correspondence
between the stretching exponent of Kohlrausch functions
and the stretching parameters of Havriliak-Negami
susceptibilities are not generally valid.

###### Key words and phrases:

PACS: 77.22.Gm,61.20.Lc,71.55.Jv, 64.70.Pf, 78.30.Ly