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Applications and Implications of Fractional Dynamics for Dielectric Relaxation

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Recent Advances in Broadband Dielectric Spectroscopy

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Abstract

This article summarizes briefly the presentation given by the author at the NATO Advanced Research Workshop on “Broadband Dielectric Spectroscopy and its Advanced Technological Applications”, held in Perpignan, France, in September 2011. The purpose of the invited presentation at the workshop was to review and summarize the basic theory of fractional dynamics (Hilfer, Phys Rev E 48:2466, 1993; Hilfer and Anton, Phys Rev E Rapid Commun 51:R848, 1995; Hilfer, Fractals 3(1):211, 1995; Hilfer, Chaos Solitons Fractals 5:1475, 1995; Hilfer, Fractals 3:549, 1995; Hilfer, Physica A 221:89, 1995; Hilfer, On fractional diffusion and its relation with continuous time random walks. In: Pekalski et al. (eds) Anomalous diffusion: from basis to applications. Springer, Berlin, p 77, 1999; Hilfer, Fractional evolution equations and irreversibility. In: Helbing et al. (eds) Traffic and granular flow’99. Springer, Berlin, p 215, 2000; Hilfer, Fractional time evolution. In: Hilfer (ed) Applications of fractional calculus in physics. World Scientific, Singapore, p 87, 2000; Hilfer, Remarks on fractional time. In: Castell and Ischebeck (eds) Time, quantum and information. Springer, Berlin, p 235, 2003; Hilfer, Physica A 329:35, 2003; Hilfer, Threefold introduction to fractional derivatives. In: Klages et al. (eds) Anomalous transport: foundations and applications. Wiley-VCH, Weinheim, pp 17–74, 2008; Hilfer, Foundations of fractional dynamics: a short account. In: Klafter et al. (eds) Fractional dynamics: recent advances. World Scientific, Singapore, p 207, 2011) and demonstrate its relevance and application to broadband dielectric spectroscopy (Hilfer, J Phys Condens Matter 14:2297, 2002; Hilfer, Chem Phys 284:399, 2002; Hilfer, Fractals 11:251, 2003; Hilfer et al., Fractional Calc Appl Anal 12:299, 2009). It was argued, that broadband dielectric spectroscopy might be useful to test effective field theories based on fractional dynamics.

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Acknowledgements

The author gratefully acknowledges financial support from the Deutsche Forschungsgemeinschaft.

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Authors and Affiliations

  1. ICP, Fakultät für Mathematik und Physik, Universität Stuttgart, 70569, Stuttgart, Germany

    R. Hilfer

  2. Institut für Physik, Universität Mainz, 55099, Mainz, Germany

    R. Hilfer

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  1. R. Hilfer
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Editors and Affiliations

  1. , Lab. de Mathématiques et Physique, Université de Perpignan, Avenue Paul Alduy 52, Perpignan, 66860, France

    Yuri P. Kalmykov

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Hilfer, R. (2013). Applications and Implications of Fractional Dynamics for Dielectric Relaxation. In: Kalmykov, Y. (eds) Recent Advances in Broadband Dielectric Spectroscopy. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5012-8_9

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