1994/02/09 by Hans C. Fogedby · 335 citations
Mathematics · Physics and Astronomy · #Distribution (mathematics) #Exponent #Force field (fiction) #Fractional Differential Equations Solutions #Langevin dynamics #Langevin equation #Lévy flight #Mathematical analysis #Mathematical physics #Mathematics #Physics #Power law #Quantum mechanics #Random walk #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1103/physreve.50.1657
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 50(2), 1657-1660 (American Physical Society) · 10 pages, Latex, IFA Report No. 94/10
arxiv created 1994/02/09 · openalex publication_date 1994/08/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider the combined effects of a power law L'evy step distribution characterized by the step index f and a power law waiting time distribution characterized by the time index g on the long time behavior of a random walker. The main point of our analysis is a formulation in terms of coupled Langevin equations which allows in a natural way for the inclusion of external force fields. In the anomalous case for f2 and g1 the dynamic exponent z locks onto the ratio f/g. Drawing on recent results on L'evy flights in the presence of a random force field we also find that this result is independent of the presence of weak quenched disorder. For d below the critical dimension dc=2f-2 the disorder is relevant, corresponding to a nontrivial fixed point for the force correlation function.