The European Physical Journal Special Topics

, Volume 191, Issue 1, pp 223–237 | Cite as

Lévy ratchet in a weak noise limit: Theory and simulation

  • I. PavlyukevichEmail author
  • B. DybiecEmail author
  • A.V. ChechkinEmail author
  • I.M. SokolovEmail author
Regular article


We study the motion of a particle in a time-independent periodic potential with broken mirror symmetry under action of a Lévy-stable noise (Lévy ratchet). We develop an analytical approach to the problem based on the asymptotic probabilistic method of decomposition proposed by P. Imkeller and I. Pavlyukevich [J. Phys. A 39, L237 (2006); Stoch. Proc. Appl. 116, 611 (2006)]. We derive analytical expressions for the quantities characterizing the particle’s motion, namely for the splitting probabilities of the first escape from a single well, for the transition probabilities to other wells and for the probability current. We pay particular attention to the interplay between the asymmetry of the ratchet potential and the asymmetry (skewness) of the Lévy noise. Extensive numerical simulations demonstrate a good agreement with the analytical predictions for sufficiently small intensities of the Lévy noise driving the particle.


European Physical Journal Special Topic Noise Intensity Stability Index Exit Time Weak Noise 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© EDP Sciences and Springer 2011

Authors and Affiliations

  1. 1.Institut für Stochastik, Friedrich–Schiller–Universität JenaJenaGermany
  2. 2.M. Smoluchowski Institute of Physics, and M. Kac Center for Complex Systems ResearchKrakówPoland
  3. 3.School of Chemistry, Tel Aviv University, Ramat Aviv, Tel Aviv 69978Ramat Aviv, Tel AvivIsrael
  4. 4.Institute for Theoretical Physics NSC KIPTKharkovUkraine

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