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Classical Properties of Infinite Quantum Open Systems

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Abstract

Long time asymptotic properties of a class of environmentally induced dynamical semigroups on arbitrary von Neumann algebras are discussed. Such a semigroup selects observables, called effective observables, which are immune to the process of decoherence and so evolve in a reversible automorphic way. In particular, it is shown that effective observables of the quantum system in the thermodynamic limit, subjected to a specific interaction with another quantum system, obey classical dynamics.

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References

  1. Alicki, R.: Phys. Rev. A 65, 034104 (2002)

    Article  Google Scholar 

  2. Araki, H.: Progr. Theor. Phys. 32, 956 (1964)

    MATH  Google Scholar 

  3. Araki, H.: Progr. Theor. Phys. 64, 719 (1980)

    MathSciNet  MATH  Google Scholar 

  4. Blanchard, Ph., et al. (eds.): Decoherence: Theoretical, Experimental and Conceptual Problems. Berlin: Springer, 2000

  5. Breuer, H.-P., Petruccione, F.: Phys. Rev. A 63, 032102 (2001)

    Article  Google Scholar 

  6. Erdös, L., Yau, H.-T.: Commun. Pure Appl. Math. 53, 667 (2000)

    Google Scholar 

  7. Frigerio, A.: Lett. Math. Phys. 2, 79 (1977)

    MATH  Google Scholar 

  8. Frigerio, A.: Commun. Math. Phys. 63, 269 (1978)

    MATH  Google Scholar 

  9. Frigerio, A., Veri, M.: Math. Z. 180, 275 (1982)

    MathSciNet  MATH  Google Scholar 

  10. Fröhlich, J., Tsai, T.-P., Yau, H.-T.: Geom. Funct. Anal. Special Volume GAFA, 57 (2000)

  11. Fröhlich, J., Tsai, T.-P., Yau, H.-T.: Commun. Math. Phys. 225, 223 (2002)

    Article  Google Scholar 

  12. Gell-Mann, M., Hartle, J.B.: Phys. Rev. D 47, 3345 (1993)

    Article  MathSciNet  Google Scholar 

  13. Ghirardi, G.C., Rimini, A., Weber, T.: Phys. Rev. D 34, 470 (1986)

    Article  MathSciNet  Google Scholar 

  14. Giulini, D., et al. (eds.): Decoherence and the Appearance of a Classical World in Quantum Theory. Berlin: Springer, 1996

  15. Groh, U.: In: One-Parameter Semigroups of Positive Operators. LNM Vol. 1184, R. Nagel (ed.), Berlin: Springer, 1986

  16. Haba, Z.: Lett. Math. Phys. 44, 121 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  17. Joos, E., Zeh, H.D.: Z. Phys. B 59, 223 (1985)

    Google Scholar 

  18. Krengel, U.: Ergodic Theorems. Berlin: Walter de Gruyter, 1985

  19. Kümmerer, B., Nagel, R.: Acta Sci. Math. 41, 151 (1979)

    Google Scholar 

  20. Landsmann, N.P.: Rev. Math. Phys. 2, 45 (1990)

    Article  Google Scholar 

  21. Ługiewicz, P., Olkiewicz, R.: J. Phys. A 35, 6695 (2002)

    Google Scholar 

  22. Majewski, W.A.: J. Stat. Phys. 55, 417 (1989)

    MathSciNet  MATH  Google Scholar 

  23. Olkiewicz, R.: Commun. Math. Phys. 208, 245 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. Olkiewicz, R.: Ann. Phys. 286, 10 (2000)

    Article  MATH  Google Scholar 

  25. Penrose, R.: In: Mathematical Physics 2000. A. Fokas et al. (eds.), London: Imperial College Press, 2000

  26. Sunder, V.S.: An Invitation to von Neumann Algebras. New York: Springer, 1986

  27. Terp, M.: J. Operator. Th. 8, 327 (1982)

    MathSciNet  MATH  Google Scholar 

  28. Walter, M.E.: Math. Scand. 37, 145 (1975)

    MATH  Google Scholar 

  29. Watanabe, S.: Hokkaido Math. J. 8, 176 (1979)

    MathSciNet  MATH  Google Scholar 

  30. Yeadon, F.J.: J. London Math. Soc. 16(2), 326 (1977)

    MATH  Google Scholar 

  31. Zurek, W.H.: Phys. Rev. D 26, 1862 (1982)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Theoretical Physics, University of Wrocław, 50-204, Wrocław, Poland

    P. Ługiewicz & R. Olkiewicz

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  1. P. Ługiewicz
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  2. R. Olkiewicz
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Correspondence to P. Ługiewicz.

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H.-T. Yau

This work was supported by the KBN research grant no 5P03B 081 21

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Ługiewicz, P., Olkiewicz, R. Classical Properties of Infinite Quantum Open Systems. Commun. Math. Phys. 239, 241–259 (2003). https://doi.org/10.1007/s00220-003-0873-x

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  • DOI: https://doi.org/10.1007/s00220-003-0873-x

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