Steady-state Lévy flights in a confined domain

S. I. Denisov, Werner Horsthemke, and Peter Hänggi
Phys. Rev. E 77, 061112 – Published 10 June 2008

Abstract

We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric Lévy flights in an infinitely deep potential well. The fractional Fokker-Planck equation for Lévy flights is derived and solved analytically in the steady state. It is shown that Lévy flights are distributed according to the beta distribution, whose probability density becomes singular at the boundaries of the well. The origin of the preferred concentration of flying objects near the boundaries in nonequilibrium systems is clarified.

  • Figure
  • Received 8 April 2008

DOI:https://doi.org/10.1103/PhysRevE.77.061112

©2008 American Physical Society

Authors & Affiliations

S. I. Denisov1,2,3, Werner Horsthemke4, and Peter Hänggi1

  • 1Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86135 Augsburg, Germany
  • 2Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
  • 3Sumy State University, 2 Rimsky-Korsakov Street, 40007 Sumy, Ukraine
  • 4Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, USA

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Issue

Vol. 77, Iss. 6 — June 2008

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