V. M. Rozenbaum, I. V. Shapochkina, L. I. Trakhtenberg, “Green's function method in the theory of Brownian motors”, UFN, 189:5 (2019), 529–543; Phys. Usp., 62:5 (2019), 496

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Uspekhi Fizicheskikh Nauk, 2019, Volume 189, Number 5, Pages 529–543
DOI: https://doi.org/10.3367/UFNr.2018.04.038347 (Mi ufn6165)

This article is cited in 24 scientific papers (total in 24 papers)

METHODOLOGICAL NOTES

Green's function method in the theory of Brownian motors

V. M. Rozenbaum^a, I. V. Shapochkina^b, L. I. Trakhtenberg^cd

^a Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Kiev
^b Belarusian State University, Minsk
^c Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow
^d Lomonosov Moscow State University

Full-text PDF (812 kB) Citations (24)

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DOI: https://doi.org/10.3367/UFNr.2018.04.038347

Abstract: We present the main results of the theory of Brownian motors obtained using the authors' approach, in which a Brownian particle moving in a slightly fluctuating potential profile is considered. By using the Green's function method, the perturbation theory in small fluctuations of potential energy is constructed. This approach allows obtaining an analytic expression for the mean particle velocity that is valid for two main types of Brownian motors (flashing and rocking ratchets) and any time dependence (stochastic or deterministic) of the fluctuations. The advantage of the proposed approach lies in the compactness of the description and, at the same time, in the variety of motor systems analyzed with its help: the overwhelming majority of known analytic results in the theory of Brownian motors follow from this expression. The mathematical derivations and analysis of those results are the main subject of these methodological notes.

Keywords: Brownian motors, ratchets, driven diffusive systems, Green's functions.

Funding agency	Grant number
Ministry of Science and Higher Education of the Russian Federation	АААА-А18-118012390045-2
Russian Foundation for Basic Research	18-57-00003 18-29-02012мк
Belarusian Republican Foundation for Fundamental Research	Ф18Р-022
Grant of President of Belarus
This study was carried out in the framework of State Assignment 0082-2018-0003 (registration number AAAA-A18-118012390045-2) and was supported by the Russian Foundation for Basic Research (projects 18-57-00003 and 18-29-02012-mk) and the Foundation for Fundamental Research of Belarus (project F18R-022). I V Sh expresses her gratitude for the support of her work through a grant from the President of the Republic of Belarus in the area of education.

Received: November 7, 2017
Revised: April 19, 2018
Accepted: April 23, 2018

English version:
Physics–Uspekhi, 2019, Volume 62, Issue 5, Pages 496–509
DOI: https://doi.org/10.3367/UFNe.2018.04.038347

Bibliographic databases:

Document Type: Article

PACS: 05.40.-a, 05.60.Cd

Language: Russian

Citation: V. M. Rozenbaum, I. V. Shapochkina, L. I. Trakhtenberg, “Green's function method in the theory of Brownian motors”, UFN, 189:5 (2019), 529–543; Phys. Usp., 62:5 (2019), 496–509

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This publication is cited in the following 24 articles:

Shazia Sadiq, Mujeeb ur Rehman, “NUMERICAL TECHNIQUE BASED ON GENERALIZED LAGUERRE AND SHIFTED CHEBYSHEV POLYNOMIALS”, jaac, 14:4 (2024), 1977
T. Ye. Korochkova, “Pulsating brownian motor with smooth modeling potentials in the framework of small fluctuation approximation”, Him. Fiz. Tehnol. Poverhni, 15:2 (2024), 159
Xiu-Hua Zhao, Z. C. Tu, Yu-Han Ma, “Engineering ratchet-based particle separation via extended shortcuts to isothermality”, Phys. Rev. E, 110:3 (2024)
Ronald Benjamin, “Noise-induced transport in a periodic square-well potential”, Phys. Scr., 99:9 (2024), 095257
V. M. Rozenbaum, I. V. Shapochkina, L. I. Trakhtenberg, “Quantum particle in a V-shaped well of arbitrary asymmetry. Brownian motors”, Phys. Usp., 67:10 (2024), 1046–1055
M. A. Taye, “Time-dependent solutions for efficiency and velocity of a Brownian heat engine that operates in a two-dimensional lattice coupled with a nonuniform thermal background”, Eur. Phys. J. B, 96:5 (2023)
V. M. Rozenbaum, I. V. Shapochkina, Y. Teranishi, H. A. Witek, L. I. Trakhtenberg, “Extremely asymmetric sawtooth potential in the ratchet theory”, J. Chinese Chemical Soc., 70:3 (2023), 209
V. M. Rozenbaum, I. V. Shapochkina, L. I. Trakhtenberg, “Tunneling mechanism for changing the motion direction of a pulsating ratchet. Temperature effect”, JETP Letters, 118:5 (2023), 369–375
V. M. Rozenbaum, M. L. Dekhtyar, I. V. Shapochkina, L. I. Trakhtenberg, “Light-driven reciprocating host-guest molecular machines”, JETP Letters, 113:11 (2021), 738–744
I. V. Shapochkina, T. Y. Korochkova, V. M. Rozenbaum, A. S. Bugaev, L. I. Trakhtenberg, “Temperature-frequency controlling the characteristics of a pulsating Brownian ratchet with slightly fluctuating potential energy”, Nonlinear Phenom. Complex Syst., 24:1 (2021), 71–83
V. M. Rozenbaum, T. Y. V. Korochkova, I. Shapochkina, L. I. Trakhtenberg, “Exactly solvable model of a slightly fluctuating ratchet”, Phys. Rev. E, 104:1 (2021), 014133
Irina V. Shapochkina, Nastassia D. Savina, Viktor M. Rozenbaum, Taisiya Ye. Korochkova, “Symmetry properties of a Brownian motor with a sawtooth potential perturbed by harmonic fluctuations”, Journal of the Belarusian State University. Physics, 2021, no. 1, 41
Irina V. Shapochkina, Nastassia D. Savina, Elena M. Zaytseva, Viktor M. Rozenbaum, Maria I. Ikim, Aleksander S. Bugaev, “Adiabatic Brownian motor with a stepwise potential perturbed by a dichotomous harmonic sygnal”, Journal of the Belarusian State University. Physics, 2021, no. 2, 71
V. M. Rozenbaum, I. V. Shapochkina, L. I. Trakhtenberg, “Adiabatic ratchet effect in systems with discrete variables”, JETP Letters, 112:5 (2020), 316–322
Yu. V. Gulyaev, A. S. Bugaev, V. M. Rozenbaum, L. I. Trakhtenberg, “Nanotransport controlled by means of the ratchet effect”, Phys. Usp., 63:4 (2020), 311–326
Yu. N. Eroshenko, “Physics news on the Internet (based on electronic preprints)”, Phys. Usp., 63:7 (2020), 730–731
T. Ye. Korochkova, N. G. Shkoda, V. M. Rozenbaum, E. V. Shakel, I. V. Shapochkina, M. I. Ikim, A. S. Bugayov, “Adiabatic temperature control of the direction of motion of a Brownian motor”, Him. Fiz. Tehnol. Poverhni, 11:3 (2020), 388
V. M. Rozenbaum, “Constructive role of chaos: Brownian motors and winning strategies in game theory”, Him. Fiz. Tehnol. Poverhni, 11:1 (2020), 100
A. D. Terets, T. Ye. Korochkova, V. M. Rozenbaum, V. A. Mashira, I. V. Shapochkina, A. N. Furs, M. I. Ikim, V. F. Gromov, “Motion reversal modeling for a Brownian particle affected by nonequilibrium fluctuations”, Him. Fiz. Tehnol. Poverhni, 11:3 (2020), 395
V. M. Rozenbaum, I. V. Shapochkina, Y. Teranishi, L. I. Trakhtenberg, “Symmetry of deterministic ratchets”, Phys. Rev. E, 100:2 (2019), 022115

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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