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Quantum particle in a V-shaped well of arbitrary asymmetry. Brownian motors

†  a, b, ‡  a, b, §  c, d
a Belarussian State University, prosp. Nezavisimosti 4, Minsk, 220030, Belarus
b Joint Institute of Dalian Polytechnic University and the Belarusian State University, Dalian, People's Republic of China
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

The dependence of the energy spectrum of a quantum particle in an infinite V-shaped potential well on its asymmetry parameter is analyzed. The relationship between the occurrence of this dependence and different depths of quantum particle penetration into classically forbidden regions under the well walls is shown. In particular, an estimate of the energy spectrum using the Bohr—Sommerfeld quantization rules, which does not take into account the particle penetration into subbarrier regions, shows that there is no dependence on the well asymmetry parameter. An exception is the transition to the case of a vertical wall, when the semiclassical approach is characterized by a special boundary condition. The results are illustrated by the dependence of the tunnel current of a Brownian motor (ratchet) with an applied fluctuating force on the asymmetry of the sawtooth potential. With a certain selection of ratchet parameters, considering zero-point oscillations describes the occurrence of a particle flow in the direction opposite to that obtained without such consideration.

Typically, an English full text is available in about 1 month from the date of publication of the original article.

Keywords: energy spectrum, asymmetric systems, Airy functions, Brownian motors, ratchets
PACS: 03.65.Ge, 05.40.−a, 05.60.Gg (all)
DOI: 10.3367/UFNe.2024.06.039704
URL: https://ufn.ru/en/articles/2024/10/f/
Citation: Rozenbaum V M, Shapochkina I V, Trakhtenberg L I "Quantum particle in a V-shaped well of arbitrary asymmetry. Brownian motors" Phys. Usp. 67 (10) (2024)

Received: 15th, February 2024, revised: 5th, May 2024, 27th, June 2024

Оригинал: Розенбаум В М, Шапочкина И В, Трахтенберг Л И «Квантовая частица в V-образной яме произвольной асимметрии. Броуновские моторы» УФН 194 1108–1117 (2024); DOI: 10.3367/UFNr.2024.06.039704

References (42) Similar articles (16) ↓

  1. V.M. Rozenbaum, I.V. Shapochkina, L.I. Trakhtenberg “Green's function method in the theory of Brownian motors” Phys. Usp. 62 496–509 (2019)
  2. E.A. Nelin “Impedance model for quantum-mechanical barrier problems” Phys. Usp. 50 293–299 (2007)
  3. Yu.M. Tsipenyuk “Zero point energy and zero point oscillations: how they are detected experimentally” Phys. Usp. 55 796–807 (2012)
  4. G.S. Golitsyn “A N Kolmogorov's 1934 paper is the basis for explaining the statistics of natural phenomena of the macrocosm” Phys. Usp. 67 80–90 (2024)
  5. A.I. Akhiezer, R.V. Polovin “Why IT IS impossible to introduce hidden parameters into quantum mechanics” Sov. Phys. Usp. 15 500–512 (1973)
  6. E.V. Shuryak “Stochastic trajectory generation by computer” Sov. Phys. Usp. 27 448–453 (1984)
  7. V.L. Ginzburg, L.P. Pitaevskii “Quantum Nyquist formula and the applicability ranges of the Callen-Welton formula” Sov. Phys. Usp. 30 168–171 (1987)
  8. V.P. Demutskii, R.V. Polovin “Conceptual problems in quantum mechanics” Sov. Phys. Usp. 35 (10) 857–896 (1992)
  9. V.I. Ritus “Finite value of the bare charge and the relation of the fine structure constant ratio for physical and bare charges to zero-point oscillations of the electromagnetic field in a vacuum” Phys. Usp. 65 468–486 (2022)
  10. V.I. Tatarskii “Example of the description of dissipative processes in terms of reversible dynamic equations and some comments on the fluctuation-dissipation theorem” Sov. Phys. Usp. 30 134–152 (1987)
  11. S.N. Gordienko “Irreversibility and the probabilistic treatment of the dynamics of classical particles” Phys. Usp. 42 573–590 (1999)
  12. O.G. Bakunin “Correlation and percolation properties of turbulent diffusion” Phys. Usp. 46 733–744 (2003)
  13. V.I. Klyatskin “Statistical topography and Lyapunov exponents in stochastic dynamical systems” Phys. Usp. 51 395–407 (2008)
  14. G.N. Bochkov, Yu.E. Kuzovlev “Fluctuation-dissipation relations: achievements and misunderstandings” Phys. Usp. 56 590–602 (2013)
  15. S.P. Efimov “Coordinate space modification of Fock's theory. Harmonic tensors in the quantum Coulomb problem” Phys. Usp. 65 952–967 (2022)
  16. S.V. Vonsovskii, M.S. Svirskii “The Klein paradox and the zitterbewegung of an electron in a field with a constant scalar potential” Phys. Usp. 36 (5) 436–439 (1993)

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