Use and Abuse of a Fractional Fokker-Planck Dynamics for Time-Dependent Driving

E. Heinsalu, M. Patriarca, I. Goychuk, and P. Hänggi
Phys. Rev. Lett. 99, 120602 – Published 21 September 2007

Abstract

We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in time-varying potential landscapes and thereby disclose the failure of the fractional Fokker-Planck equation (FFPE) in its commonly used form when generalized in an ad hoc manner to time-dependent forces. A modified FFPE (MFFPE) is rigorously derived, being valid for a family of dichotomously alternating force fields. This MFFPE is numerically validated for a rectangular time-dependent force with zero average bias. For this case, subdiffusion is shown to become enhanced as compared to the force free case. We question, however, the existence of any physically valid FFPE for arbitrary varying time-dependent fields that differ from this dichotomous varying family.

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  • Received 14 March 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.120602

©2007 American Physical Society

Authors & Affiliations

E. Heinsalu1,2, M. Patriarca1,2, I. Goychuk2, and P. Hänggi2

  • 1Institute of Theoretical Physics, Tartu University, Tähe 4, 51010 Tartu, Estonia
  • 2Institut für Physik, Universität Augsburg, Universitätsstr. 1, D-86135 Augsburg, Germany

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Issue

Vol. 99, Iss. 12 — 21 September 2007

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