ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


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Sanin A. L., Smirnovsky A. A. Quantum spatially confined oscillator in system with friction and feedback. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 2, pp. 18-54. DOI: 10.18500/0869-6632-2008-16-2-18-54

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Language: 
Russian
Article type: 
Article
UDC: 
530.145

Quantum spatially confined oscillator in system with friction and feedback

Autors: 
Sanin Andrej Leonardovich, Peter the Great St. Petersburg Polytechnic University
Smirnovsky Aleksandr Andreevich, Peter the Great St. Petersburg Polytechnic University
Abstract: 

The dynamics of quantum wave packets in one-dimensional system with spatially confined quadratic potential, feedback and friction was numerically investigated in the context of the Schrodinger–Langevin–Kostin equation. The coherent oscillations are ¨ possible in the system under determined values of the feedback force and friction coefficient. There are the critical values of these quantities when the packet oscillations become complicated, the uncertainty product increases sharply, oscillates, but the Fourier-spectrum is everywhere dense. 

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Reference: 
  1. Stockmann HJ. Quantum Chaos. Cambridge: Cambridge University Press; 1999. 368 p. DOI: 10.1017/CBO9780511524622.
  2. Demikhovsky VY, Malyshev AI. Arnold quantum diffusion in a channel with a corrugated boundary in the presence of an alternating electric field. Izvestiya VUZ. Applied Nonlinear Dynamics. 2004;12(5):3 (in Russian).
  3. Sankaranarayanan R, Lakshminarayan A, Sheorey VB. Quantum chaos of a particle in a square well: competing length scales and dynamical localization. Phys. Rev. E. 2001;64(4):046210. DOI: 10.1103/PhysRevE.64.046210.
  4. Belyaev MV, Lazerson AG. Complex dynamics of a non-autonomous quantum oscillator. Izvestiya VUZ. Applied Nonlinear Dynamics. 2003;11(2):25–33 (in Russian).
  5. Mott N, Sneddon I. Wave Mechanics and Its Applications. Oxford and the Clarendon Press; 1948. 427 p.
  6. Bagmanov AT, Sanin AL. Resonances of a spatially constrained quantum oscillator. Telecommunications and Radio Engineering. 2005;(12):46–54 (in Russian).
  7. Rabinovich MI, Trubetskov DI. Oscillations and Waves in Linear and Nonlinear Systems. Berlin: Springer; 1989. 578 p. DOI: 10.1007/978-94-009-1033-1.
  8. Lichtenberg AJ, Lieberman MA. Regular and Chaotic Dynamics. NY: Springer; 1992. 692 p. DOI: 10.1007/978-1-4757-2184-3.
  9. Landa PS. Nonlinear Oscillations and Waves in Dynamical Systems. Dordrecht: Springer; 1996. 544 p. DOI: 10.1007/978-94-015-8763-1.
  10. Kostin MD. On the Schrodinger–Langevin equation. J. Chem. Phys. 1972;57(9):3589–3591. DOI: 10.1063/1.1678812.
  11. Sanin AL, Smirnovskij AA. Driven oscillations of quantum wave packets in system with friction, quadratic potential and impenetrable walls. Izvestiya VUZ. Applied Nonlinear Dynamics. 2007;15(4):68–83 (in Russian). DOI: 10.18500/0869-6632-2007-15-4-68-83.
  12. Sanin AL, Smirnovsky AA. Oscillatory motion in confined potential systems with dissipation in the context of the Schrodinger–Langevin–Kostin equation. Phys. Lett. A. 2007;372(1):21–27. DOI: 10.1016/j.physleta.2007.07.019.
  13. Sanin AL, Smirnovsky AA. Influence of dissipation on quantum wave dynamics in confined potential systems. Proc. SPIE. 2007;6597:659704. DOI: 10.1117/12.726707.
  14. Smirnovsky AA. The Schrödinger – Langevin – Kostin equation with a dissipative term in integral form. In: Aleshkovsky IA, Kostylev PN, editors. Proceedings of the XIV International Conference of Students, Postgraduates and Young Scientists "Lomonosov". Moscow: Publishing Center of the Faculty of Journalism of Lomonosov Moscow State University; 2007 (in Russian).
  15. Grindlay J. On an application of a generalization of the discrete Fourier transform to short time series. Can. J. Phys. 2001;79(5):857–868. DOI: 10.1139/cjp-79-5-857.
  16. Igarashi A, Yamada HS. Quantum dynamics and delocalization in coherently driven one-dimensional double-well system. arXiv: cond-mat/0508483.
Received: 
21.12.2007
Accepted: 
06.02.2008
Published: 
30.04.2008
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