Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 62: Glasses and Glass transition (joint session DY/CPP)

DY 62.1: Talk

Friday, April 5, 2019, 10:00–10:15, H19

Unified Formulation of Fractional Relaxation — •Tillmann Kleiner and Rudolf Hilfer — Institut für Computerphysik, Universität Stuttgart

Susceptibility functions that involve stretching exponents which are derived from fractional dynamics [1] reproduce the excess wing of α-relaxation peaks that has been observed in dielectric spectra of glass forming materials [2]. The contemporary formulation of fractional dynamics requires two distinct approaches to describe the relaxation motion and the response of the system to periodic excitations. The former uses fractional Liouville-Caputo derivatives in the time domain and the latter multiplication with the susceptibility function in the frequency domain. Both approaches impose severe restrictions on the past history of the involved electric field that are unrealistic in an experimental situation. Due to the occurrence of memory effects this poses a serious problem. In this contribution a unified description of fractional dynamics is presented where fractional derivatives are defined using distributional convolution. The resulting response functions are stretched multinomial Mittag-Leffler functions. This formulation extends the mentioned approaches to all experimentally relevant situations in a consistent way and exposes a high degree of convenience.

[1] R. Hilfer, Analysis 36, 49-64 (2016)

[2] F. Kremer and A. Loidl, The Scaling of Relaxation Processes,

    Springer, (2018)