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Quantum open systems as random classical dynamical systems

Part I: Lectures
Part of the Lecture Notes in Physics book series (LNP, volume 457)

Abstract

We discuss an interaction of a quantum oscillator with a heat bath of harmonic oscillators. We define a classical Markov process whose correlations coincide with correlations of the quantum oscillator in a heat bath. In this way we replace a quantum non-commutative problem by a classical commutative one. In this framework we discuss briefly dissipation, noise,spontaneous localization and decoherence in quantum mechanics.

Keywords

Density Matrix Coherent State Stochastic Differential Equation Langevin Equation Heat Bath 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    W.H. Louisell, Quantum Statistical Properties of Radiation, Wiley, New York, 1973.Google Scholar
  2. 2.
    H. Haken, Light, waves, photons, atoms, Springer, 1986.Google Scholar
  3. 3.
    G.S. Agarwal, Quantum Statistical Theories of Spontaneous Emission and Their Relation to Other Approaches, Springer, 1974.Google Scholar
  4. 4.
    L. Accardi and Y.G. Lu, in Quantum Probability VII, Springer Lecture Notes in Math., 1992.Google Scholar
  5. 5.
    R. Benguria and M. Kac, Phys. Rev. Lett. 46, 1 (1981).Google Scholar
  6. 6.
    I.R. Senitzky, Phys. Rev. 119, 670 (1960)124, 642(1961).Google Scholar
  7. 7.
    N.G. van Kampen, in Stochasticity and Quantum Chaos, ed. by Z. Haba et al, Kluwer, 1995, see also J. Stat. Phys. 78, 299(1995).Google Scholar
  8. 8.
    M. Sargent III, M.O. Scully and W.E. Lamb, Laser Physics, Addison-Wesley, 1974.Google Scholar
  9. 9.
    Z. Haba, Phys. Lett. 175A, 371 (1993).Google Scholar
  10. 10.
    Z. Haba, Phys. Lett. 189A, 261 (1994).Google Scholar
  11. 11.
    Z.Haba, J. Phys. A27, 6457 (1994).Google Scholar
  12. 12.
    Z. Haba, Coherent States and Quantum Dynamics of Non-linear Systems, subm. for publication.Google Scholar
  13. 13.
    W.G. Unruh and W.H. Zurek, Phys. Rev. D40, 1071 (1989); M. Gell-Mann and J.B. Hartle, in Complexity, Entropy and the Physics of Information, ed. W.H. Zurek, Addison-Wesley, 1990.Google Scholar
  14. 14.
    J.P. Paz, S. Habib and W.H. Zurek, Phys. Rev. D47, 488 (1993).Google Scholar
  15. 15.
    I.R. Senitzky, Phys. Rev. A48, 4629 (1993)Google Scholar
  16. 16.
    I.I. Gikhmana and A.V. Skorohod, Stochastic Differential Equations, Springer, New York, 1972.Google Scholar
  17. 17.
    M. Freidlin, Functional Integration and Partial Differential Equations, Princeton, 1985.Google Scholar
  18. 18.
    G.W. Ford, J.T. Lewis and R.F. O'Connell, Phys. Rev. A37, 4419 (1988).Google Scholar
  19. 19.
    A.O. Caldeira and A.J. Leggett, Physica A121, 587 (1983).Google Scholar
  20. 20.
    L.E. Ballentine, Phys. Rev. A43, 9 (1991)Google Scholar
  21. 20.a
    E. Joos and H.D. Zeh, Z. Phys. B59, 223 (1985)Google Scholar
  22. 20.b
    L. Diosi, Phys. Rev. A40, 1165 (1985).Google Scholar
  23. 21.
    G.C. Ghirardi, P. Pearl and A. Rimini, Phys. Rev. A42, 78 (1990).Google Scholar
  24. 22.
    N. Gisin and I.C. Percival, J. Phys. A25, 5677 (1992).Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Z. Haba
    • 1
  1. 1.Institute of Theoretical PhysicsUniversity of WroclawWroclawPoland

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