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.

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 URL: https://ufn.ru/en/articles/2019/5/e/ 000477641200005 2-s2.0-85070662806 2019PhyU...62..496R 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) BibTexBibNote ® (generic) BibNote ® (RIS)MedlineRefWorks TY JOUR TI Green's function method in the theory of Brownian motors AU Rozenbaum, V. M. AU Shapochkina, I. V. AU Trakhtenberg, L. I. PB Physics-Uspekhi PY 2019 JO Physics-Uspekhi JF Physics-Uspekhi JA Phys. Usp. VL 62 IS 5 SP 496-509 UR https://ufn.ru/en/articles/2019/5/e/ ER https://doi.org/10.3367/UFNe.2018.04.038347 Received: 7th, November 2017, revised: 19th, April 2018, accepted: 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