Journal of Russian Laser Research

, Volume 26, Issue 4, pp 259–272 | Cite as

Entangled Gaussian States of a Two-Dimensional Nonstationary Damped Oscillator

  • V. I. Man’ko
  • O. V. Pilyavets
Article

Abstract

The evolution of some Gaussian states of a two-dimensional quantum oscillator with varying frequency and friction is considered. An analysis related to the entanglement evolution of quantum states is carried out. The symplectic-tomography representation is used.

Keywords

quantum friction entanglement coherent state quantum correlations 

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References

  1. 1.
    K. Husimi, Prog. Theor. Phys., 9, 381 (1953).Google Scholar
  2. 2.
    V. V. Dodonov, Phys. Lett. A, 213, 219 (1996).CrossRefMathSciNetGoogle Scholar
  3. 3.
    V. V. Dodonov, A. B. Klimov, and V. I. Man’ko, Phys. Lett. A, 149, 225 (1990); J. Sov. Laser Res., 12, 439 (1991).CrossRefGoogle Scholar
  4. 4.
    V. V. Dodonov, A. B. Klimov and D. E. Nikonov, J. Math. Phys., 34, 2742 (1993).CrossRefGoogle Scholar
  5. 5.
    V. V. Dodonov and A. B. Klimov, Phys. Lett. A, 167, 309 (1992); J. Sov. Laser Res., 13, 230 (1992).CrossRefGoogle Scholar
  6. 6.
    S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996); Found. Phys., 27, 801 (1997).CrossRefGoogle Scholar
  7. 7.
    P. Caldirola, Nuovo Cimento, 18, 393 (1941).Google Scholar
  8. 8.
    E. Kanai, Prog. Theor. Phys., 3, 440 (1948).Google Scholar
  9. 9.
    H. Dekker, Phys. Repts., 80, 1 (1981).CrossRefGoogle Scholar
  10. 10.
    R. W. Hasse, J. Math. Phys., 16, 2005 (1975).CrossRefGoogle Scholar
  11. 11.
    H. Bateman, Phys. Rev., 38, 815 (1931).CrossRefGoogle Scholar
  12. 12.
    V. V. Dodonov and V. I. Man’ko, Nuovo Cimento B, 44, 265 (1978); V. V. Dodonov and V. I. Man’ko, Phys. Rev. A, 20, 550 (1979).Google Scholar
  13. 13.
    J. Messer, Acta Phys. Aust., 50, 75 (1979).Google Scholar
  14. 14.
    I. R. Svin’in, Teor. Mat. Fiz., 27, 270 (1976).Google Scholar
  15. 15.
    M. D. Kostin, J. Chem. Phys., 57, 3589 (1973).CrossRefGoogle Scholar
  16. 16.
    M. Razavy, Z. Phys. B, 26, 201 (1977).CrossRefGoogle Scholar
  17. 17.
    E. B. Davies, Quantum Theory of Open Systems, Academic Press, New York (1976).Google Scholar
  18. 18.
    E. Schrodinger, Naturwissenschaften, 23, 807 (1935).CrossRefGoogle Scholar
  19. 19.
    V. V. Dodonov, A. S. M. De Castro, and S. S. Mizrahi, Phys. Lett. A, 296, 531 (2002); A. S. M. De Castro and V. V. Dodonov, J. Russ. Laser Res., 23, 93 (2003); A. S. M. De Castro and V. V. Dodonov, J. Opt. B: Quantum Semiclass. Opt., 5, 593 (2003).CrossRefGoogle Scholar
  20. 20.
    M. A. Man’ko, J. Russ Laser Res., 21, 421 (2000); 22, 168 (2001).Google Scholar
  21. 21.
    V. V. Dodonov and V. I. Man’ko, Invariants and the Evolution of Nonstationary Quantum Systems, Proceedings of the Lebedev Physical Institute, Nauka, Moscow (1987), Vol. 183 [translated by Nova Science, New York (1989)].Google Scholar
  22. 22.
    O. V. Man’ko, “Quantum tomography and the classical propagator for quadratic quantum systems,” Preprint IC/99/16, ICTP, Trieste, Italy (1996).Google Scholar
  23. 23.
    O. V. Man’ko, V. I. Man’ko, and G. Marmo, Phys. Scr., 62, 446 (2000); J. Phys. A: Math. Gen., 35, 699 (2002).CrossRefGoogle Scholar
  24. 24.
    E. Wigner, Phys. Rev., 40, 749 (1932).CrossRefGoogle Scholar
  25. 25.
    O. V. Man’ko, V. I. Man’ko, G. Marmo, Anil Shaji, E. C. G. Sudarshan, and F. Zaccaria, Phys. Lett. A, 339, 194 (2005).CrossRefGoogle Scholar
  26. 26.
    O. V. Manko and V. I. Man’ko, J. Russ. Laser Res., 25, 477 (2004); “Classical mechanics is not the h → 0 limit of quantum mechanics,” Los Alamos ArXiv quant-ph/0407183 (2004).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • V. I. Man’ko
    • 1
  • O. V. Pilyavets
    • 2
  1. 1.P. N. Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia
  2. 2.Moscow Institute of Physics and Technology (State University)Dolgoprudny, Moscow RegionRussia

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