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Lévy ratchet in a weak noise limit: Theory and simulation

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Abstract.

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.

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Authors and Affiliations

  1. Institut für Stochastik, Friedrich–Schiller–Universität Jena, Ernst–Abbe–Platz 2, 07743, Jena, Germany

    I. Pavlyukevich

  2. M. Smoluchowski Institute of Physics, and M. Kac Center for Complex Systems Research, Jagiellonian University, ul. Reymonta 4, 30-059, Kraków, Poland

    B. Dybiec

  3. School of Chemistry, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Ramat Aviv, Tel Aviv, Israel

    A.V. Chechkin

  4. Institute for Theoretical Physics NSC KIPT, Akademicheskaya st. 1, Kharkov, 61108, Ukraine

    I.M. Sokolov

Authors
  1. I. Pavlyukevich
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  2. B. Dybiec
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  3. A.V. Chechkin
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  4. I.M. Sokolov
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Corresponding authors

Correspondence to I. Pavlyukevich, B. Dybiec, A.V. Chechkin or I.M. Sokolov.

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Pavlyukevich, I., Dybiec, B., Chechkin, A. et al. Lévy ratchet in a weak noise limit: Theory and simulation. Eur. Phys. J. Spec. Top. 191, 223–237 (2010). https://doi.org/10.1140/epjst/e2010-01352-6

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  • DOI: https://doi.org/10.1140/epjst/e2010-01352-6

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