Abstract:
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 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.
The study was partially carried out within the framework of the State Scientific Research Program of the Republic of Belarus (Project 1.17.1.), as well as within the framework of the task of the Ministry of Science and Higher Education of the Russian Federation (registration number 122040500071-0).
Received:February 15, 2024 Revised:May 5, 2024 Accepted: June 27, 2024
Citation:
V. M. Rozenbaum, I. V. Shapochkina, L. I. Trakhtenberg, “Quantum particle in a V-shaped well of arbitrary asymmetry. Brownian motors”, UFN, 194:10 (2024), 1108–1117; Phys. Usp., 67:10 (2024), 1046–1055