Fractional diffusion in periodic potentials

  • Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two quadratures. This theoretical result is corroborated by numerical simulations for different shapes of the periodic potential. Normal and fractional spreading processes are contrasted via their time evolution of the corresponding probability densities in state space. While there are distinct differences occurring at small evolution times, a re-scaling of time yields a mutual matching between the long-time behaviors of normal and fractional diffusion.

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Author:E. Heinsalu, Marco Patriarca, Igor GoychukORCiDGND, Peter HänggiORCiDGND
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Publishing Institution:Universität Augsburg
Release Date:2006/08/30
Tag:Fractional diffusion; space-periodic potentials
GND-Keyword:Anomale Diffusion; Periodisches Potenzial
Source:J. Phys. - Condensed Matter (2006), in press
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik / Lehrstuhl für Theoretische Physik I
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik