Symmetry properties of a Brownian motor with a sawtooth potential perturbed by harmonic fluctuations

  • Irina V. Shapochkina Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0002-6962-7931
  • Nastassia D. Savina Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
  • Viktor M. Rozenbaum Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, 17 Generala Naumova Street, Kyiv 03164, Ukraine https://orcid.org/0000-0003-2889-3915
  • Taisiya Ye. Korochkova Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, 17 Generala Naumova Street, Kyiv 03164, Ukraine
DOI: https://doi.org/10.33581/2520-2243-2021-1-41-49

Abstract

We present a study of general symmetry properties of a Brownian ratchet model. The study is based both on constructing chains of symmetry transformations reflecting explicit and hidden symmetries of the average ratchet velocity as a functional of the spatially periodic potential energy of a nanoparticle and on taking into account the symmetry types of periodic functions that are components of the potential energy of an additive-multiplicative form. A ratchet with a sawtooth stationary potential profile, dichotomously perturbed by a spatially harmonic signal, is investigated. Conclusions are made on both the possibility of occurrence of the ratchet effect and its direction for given values of the asymmetry parameter of the sawtooth profile, phase shifts of the control component, and frequencies of temporal fluctuations. These conclusions have been obtained only on the basis of symmetry transformations; that demonstrates the predictive value of the approach presented. The results of the symmetry analysis are confirmed by numerical simulation of the functioning of a ratchet with dichotomous stochastic spatially periodic fluctuations of the nanoparticle potential energy.

Author Biographies

Irina V. Shapochkina, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

PhD (physics and mathematics), docent; associate professor at the department of computer modeling, faculty of physics

Nastassia D. Savina, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

student at the faculty of physics

Viktor M. Rozenbaum, Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, 17 Generala Naumova Street, Kyiv 03164, Ukraine

doctor of science (physics and mathematics), full professor; head of the department of theoretical and experimental physics of nanosystems

Taisiya Ye. Korochkova, Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, 17 Generala Naumova Street, Kyiv 03164, Ukraine

PhD (physics and mathematics); senior researcher at the department of theoretical and experimental physics of nanosystems

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Published
2021-02-09
Keywords: diffusion transport, diffusional dynamics, ratchet systems, Brownian motors, symmetry, sawtooth potential, harmonic fluctuations
Supporting Agencies This work was supported by the Belarusian Republican Foundation for Fundamental Research (project No. F20R-032).
How to Cite
Shapochkina, I. V., Savina, N. D., Rozenbaum, V. M., & Korochkova, T. Y. (2021). Symmetry properties of a Brownian motor with a sawtooth potential perturbed by harmonic fluctuations. Journal of the Belarusian State University. Physics, 1, 41-49. https://doi.org/10.33581/2520-2243-2021-1-41-49
Issue
No 1 (2021): Journal of the Belarusian State University. Physics
Section
Theoretical Physics

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