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

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

2007-03-15

arxiv.org/abs/cond-mat/0703420v2

Phys. Rev. Lett. 99, 120602 (2007)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.99.120602

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 {\it 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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