2007/03/31 by E. Heinsalu, Els Heinsalu, Marco Patriarca +5 · 95 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Dynamics (music) #Fokker–Planck equation #Fractional Differential Equations Solutions #Physics #Quantum mechanics #Statistical Mechanics and Entropy #Statistical physics #Zero (linguistics) #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physrevlett.99.120602
published in Physical Review Letters 99(12), 120602 (American Physical Society) · 4 pages, 2 figures
arxiv created 2007/05/18 · openalex publication_date 2007/09/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.