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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

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.

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