Methodological notes

Green's function method in the theory of Brownian motors

 a,  b,  c, d
a Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Ghenerala Naumova str. 17, Kiev, 03164, Ukraine
b Belarussian State University, prosp. F. Scoriny 4, Minsk, 220050, Belarus
c Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences, ul. Kosygina, 4, Moscow, 119991, Russian Federation
d Lomonosov Moscow State University, Vorobevy Gory, Moscow, 119991, Russian Federation

We present the main results of the theory of Brownian motors obtained using the author approach in which a Brownian particle moving in a slightly fluctuating potential profile is considered. By the Green's function method, the perturbation theory in small fluctuations of potential energy is constructed. This approach allows obtaining an analytical expression for the average particle velocity that is valid for two main types of Brownian motors (flashing and rocking ratchets) and any (stochastic or deterministic) time dependence 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 analytical results in the theory of Brownian motors follow from this expression. The mathematical derivations and analysis of those results forms the main content of these methodological notes.

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Keywords: Brownian motors, ratchets, driven diffusive systems, Green's functions
PACS: 05.40.−a, 05.60.Cd (all)
DOI: 10.3367/UFNe.2018.04.038347
Citation: Rozenbaum V M, Shapochkina I V, Trakhtenberg L I "Green's function method in the theory of Brownian motors" Phys. Usp. 62 496–509 (2019)
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RT Journal
T1 Green's function method in the theory of Brownian motors
A1 Rozenbaum,V.M.
A1 Shapochkina,I.V.
A1 Trakhtenberg,L.I.
PB Physics-Uspekhi
PY 2019
FD 10 May, 2019
JF Physics-Uspekhi
JO Phys. Usp.
VO 62
IS 5
SP 496-509
DO 10.3367/UFNe.2018.04.038347

Received: 7th, November 2017, revised: 19th, April 2018, 23rd, April 2018

Оригинал: Розенбаум В М, Шапочкина И В, Трахтенберг Л И «Метод функций Грина в теории броуновских моторов» УФН 189 529–543 (2019); DOI: 10.3367/UFNr.2018.04.038347

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