Use and abuse of a fractional Fokker-Planck dynamics for time-dependent driving.

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.

• Publication year

  2007

• Venue

  Physical Review Letters

• Publication date

  2007-03-15

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1103/PhysRevLett.99.120602arXiv cond-mat/0703420PMID 17930490
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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