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Adiabatic Ratchet Effect in Systems with Discrete Variables

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Abstract

An adiabatic theory of the ratchet effect in various systems described by random transitions between discrete states has been developed. The theory is based on the development of a discrete analog of the Parrondo lemma, which is one of the fundamental relations of the theory of ratchet systems allowing the calculation of integral fluxes in time intervals from the initial to final (equilibrium) distributions. Correspondence between the transition probabilities and the parameters of the potential profile, in which the hopping motion is described by the developed theory and is a low-temperature limit of continuous motion, has been proposed. The rate of the ratchet effect calculated by the proposed theory is well confirmed by a numerical simulation. The developed approach makes it possible to study the characteristics of the operation of Brownian motors of various natures by simple methods.

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Authors and Affiliations

  1. Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Kyiv, 03164, Ukraine

    V. M. Rozenbaum

  2. Department of Physics, Belarusian State University, Minsk, 220050, Belarus

    I. V. Shapochkina

  3. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, 119991, Russia

    L. I. Trakhtenberg

  4. Moscow State University, Moscow, 119991, Russia

    L. I. Trakhtenberg

Authors
  1. V. M. Rozenbaum
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  2. I. V. Shapochkina
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  3. L. I. Trakhtenberg
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Corresponding author

Correspondence to V. M. Rozenbaum.

Additional information

Russian Text © The Author(s), 2020, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2020, Vol. 112, No. 5, pp. 332–339.

Funding

This work was supported by the Federal Agency for Scientific Organizations of the Russian Federation (state assignment no. 0082-2018-0003, registration no. AAAA-A18-118012390045-2), by the Russian Foundation for Basic Research (project nos. 20-57-00007 and 18-29-02012-mk), and by the Belarusian Republican Foundation for Fundamental Research (project no. F20R-032).

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Rozenbaum, V.M., Shapochkina, I.V. & Trakhtenberg, L.I. Adiabatic Ratchet Effect in Systems with Discrete Variables. Jetp Lett. 112, 316–322 (2020). https://doi.org/10.1134/S0021364020170075

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  • DOI: https://doi.org/10.1134/S0021364020170075

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