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Experimental evidence for fractional time evolution in glass forming materials

R. Hilfer
1.: ICA-1, Universität Stuttgart, 70569 Stuttgart, Germany
2.: Institut für Physik, Universität Mainz, 55099 Mainz, Germany

The infinitesimal generator of time evolution in the standard equation for exponential (Debye) relaxation is replaced with the infinitesimal generator of composite fractional translations. Composite fractional translations are defined as a combination of translation and the fractional time evolution introduced in Physica A, vol 221, page 89 (1995). The fractional differential equation for composite fractional relaxation is solved. The resulting dynamical susceptibility is used to fit broad band dielectric spectroscopy data of glycerol. The composite fractional susceptibility function can exhibit an asymmetric relaxation peak and an excess wing at high frequencies in the imaginary part. Nevertheless it contains only a single stretching exponent. Qualitative and quantitative agreement with dielectric data for glycerol is found that extends into the excess wing. The fits require fewer parameters than traditional fit functions and can extend over up to 13 decades in frequency.

Key words and phrases:
glassy dynamics, fractional derivatives, dielectric spectroscopy, glass forming materials, glycerol, fractional calculus
PACS: 77.22.Gm,61.20.Lc, 02.90+p, 71.55.Jv, 78.30.Ly