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 rule, 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 obtained results are illustrated by the dependence of the tunnel current of a Brown„ian 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.

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/ 2-s2.0-85211493699 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 1046–1055 (2024) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 15th, February 2024, revised: 5th, May 2024, accepted: 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