DRIVEN OSCILLATIONS OF QUANTUM WAVE PACKETS IN SYSTEM WITH FRICTION, QUADRATIC POTENTIAL AND IMPENETRABLE WALLS
Cite this article as:
Sanin А. L., Smirnovsky А. А. DRIVEN OSCILLATIONS OF QUANTUM WAVE PACKETS IN SYSTEM WITH FRICTION, QUADRATIC POTENTIAL AND IMPENETRABLE WALLS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 4, pp. 68-83. DOI: https://doi.org/10.18500/0869-6632-2007-15-4-68-83
The quantum dissipative system with quadratic potential confined by infinite walls of well and subjected to impulse pump was investigated in detail. The numerical simulation was carried out in context of the Schrodinger-Langevin-Kostin equation. The propagation of quantum wave packets, calculations of phase trajectories and mappings, dynamical averages, frequency spectra have been performed and discussed. These data allow to state the existence of the stable oscillatory regimes and correspondence with classic analogous systems.
1. Ford G.W., Kac M., and Mazur P. Statistical mechanics of assemblies of coupled oscillators // J. Math. Phys. 1965. Vol. 6, No 4. P. 504.
2. Kostin M.D. On the Schrodinger-Langevin equation // J. Chem. Phys. 1972. ̈ Vol. 57(9). P. 3589.
3. Wagner Heinz-Jurgen. Schrodinger quantization and variational principles of dissi-pative quantum theory // Z. Phys. B. 1994. Vol. 95. P. 261.
4. Albrecht K. A new class of Schrodinger operators for quantized friction // Phys.Lett. 1975. Vol. 56B, No 2. P. 127.
5. Hasse R.W. On the quantum mechanical treatment of dissipative systems // J. Math. Phys. 1975. Vol. 16, No 10. P. 2005.
6. Doebner H.-D., Goldin G.A. Introducing nonlinear gauge transformation in a family of nonlinear Schrodinger equations // Phys. Rev. A. 1996. Vol. 54, No 5. P. 3764. ̈
7. Wysocki R.J. Hydrodynamic quantization of mechanical systems // Phys. Rev. A. 2005. Vol. 72. P. 032113-1.
8. Van P., F ́ ul ̈ op T. ̈ Stability of stationary solutions of the Schrodinger-Langevin equa-tion // Phys. Lett. A. 2004. Vol. 323. P. 374.
9. Санин А.Л. Квантовый транспорт электрона в пространстве с однородным положительным зарядом и световой волной // Оптика и спектроскопия. 1994. Т. 77, No 5. С. 822.
10. Андронов А.А., Витт А.А., Хайкин С.Э. Теория колебаний. М.: ГИФМЛ, 1959.
11. Ланда П.С. Автоколебания в системах с конечным числом степеней свободы. М.: Наука, 1980.
12. Рабинович М.И., Трубецков Д.И. Введение в теорию колебаний. М.: Наука, 1984.
13. Мигулин В.В., Медведев В.И., Мустель Е.Р., Парыгин В.Н. Основы теории колебаний. М.: Наука, 1988.
14. Ланда П.С. Нелинейные колебания и волны. М.: Наука – Физматлит, 1997.
15. Карлов Н.В., Кириченко Н.А. Колебания, волны, структуры. М.: Физматлит, 2001.
16. Эрроусмит Д., Плейс К. Обыкновенные дифференциальные уравнения. Качественная теория с приложениями. М.: Мир, 1986.
17. Grindlay J. On an application of a generalization of the discrete Fourier transform to short time series // Can. J. Phys. 2001. Vol. 79. P. 857.
18. Mott N., Sneddon I. Wave mechanics and its applications. Oxford and the Clarendon Press. 1948, 427 p.
19. Багманов А.Т., Санин А.Л. Квантовая динамика микрочастицы в одномерных системах // Научно-технические ведомости СПбГТУ. 2005. No 4. С. 7.
20. Багманов А.Т., Санин А.Л. Резонансы пространственно ограниченного квантового осциллятора // Успехи современной радиоэлектроники. 2005. No 12. С. 46.
21. Ushveridze A.G. Dissipative quantum mechanics. A special Doebner-Goldin equation, its properties and exact solutions // Phys. Lett. A. 1994. Vol. 185. P. 123.
22. Ushveridze A.G. The special Doebner-Goldin equation as a fundamental equation of dissipative quantum mechanics // Phys. Lett. A. 1994. Vol. 185. P. 128.
23. Smirnovsky A.A., Sanin A.L. Temporal resonances and structures in quantum systems under dissipation // Proceedings of SPAS jointly with UWM. Tenth Intern. Workshop on NDTSC-2006. 5-8 July 2006. Univ. of Warmia and Mazury in Olsztyn. Olsztyn, Poland. 2006. Vol. 10. P. 43.
BibTeX
author = {А. L. Sanin and А. А. Smirnovsky },
title = {DRIVEN OSCILLATIONS OF QUANTUM WAVE PACKETS IN SYSTEM WITH FRICTION, QUADRATIC POTENTIAL AND IMPENETRABLE WALLS},
year = {2007},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {15},number = {4},
url = {https://old-andjournal.sgu.ru/en/articles/driven-oscillations-of-quantum-wave-packets-in-system-with-friction-quadratic-potential-and},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2007-15-4-68-83},pages = {68--83},issn = {0869-6632},
keywords = {-},
abstract = {The quantum dissipative system with quadratic potential confined by infinite walls of well and subjected to impulse pump was investigated in detail. The numerical simulation was carried out in context of the Schrodinger-Langevin-Kostin equation. The propagation of quantum wave packets, calculations of phase trajectories and mappings, dynamical averages, frequency spectra have been performed and discussed. These data allow to state the existence of the stable oscillatory regimes and correspondence with classic analogous systems. }}