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Irreversible Quantum Dynamics pp 65–79Cite as

Concepts and Methods in the Theory of Open Quantum Systems

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Part of the book series: Lecture Notes in Physics ((LNP,volume 622))

Abstract

The central physical concepts and mathematical techniques used in the theory of open quantum systems are reviewed. Particular emphasis is laid on the interrelations of apparently different approaches. Starting fromthe appropriate characterization of the quantumstatistical ensembles naturally arising in the description of open quantum systems, the corresponding dynamical evolution equations are derived for the Markovian as well as for the non-Markovian case.

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References

  1. C. Cohen-Tannoudj, J. Dupont-Roc, G. Grynberg, Atom-Photon Interactions (John Wiley, New York, 1998).

    Google Scholar 

  2. H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).

    MATH  Google Scholar 

  3. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994).

    MATH  Google Scholar 

  4. U. Weiss, Quantum Dissipative Systems, Volume 2 of Series in Modern Condensed Matter Physics (World Scientific, Singapore, 1999).

    Google Scholar 

  5. P. Pechukas and U. Weiss (guest editors), Quantum Dynamics of Open Systems, Chemical Physics, Special Issue, Vol. 268, Nos. 1–3 (2001).

    Google Scholar 

  6. I. O. Kulik and R. Ellialtioglu (Eds.), Quantum Mesoscopic Phenomena and Mesoscopic Devices in Microelectronics, NATO Series, Series C: Mathematical and Physical Sciences, Vol. 559 (Kluwer Academic Publishers, Dordrecht, 2000).

    Google Scholar 

  7. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 1997).

    Google Scholar 

  8. D.D. Awschalom, D. Loss, and N. Samarth (eds.), Semiconductor Spintronics and Quantum Computation, Series on Nanoscience and Technology, (Springer-Verlag, Berlin, 2002).

    Google Scholar 

  9. V. B. Braginsky and F. Ya. Khalili, Quantum Measurement (Cambridge University Press, Cambridge, 1992).

    Book  MATH  Google Scholar 

  10. D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer-Verlag, Berlin, 1996).

    MATH  Google Scholar 

  11. R. Alicki and M. Fannes, Quantum Dynamical Systems (Oxford University Press, Oxford, 2001).

    Book  MATH  Google Scholar 

  12. A. Royer, Phys. Rev. A, 6 (1972) 1741.

    Article  ADS  Google Scholar 

  13. A. Royer, this volume.

    Google Scholar 

  14. N. G. van Kampen, Physica, 74 (1974) 215–238; 74 (1974) 239-247.

    Article  ADS  MathSciNet  Google Scholar 

  15. S. Nakajima, Progr. Theor. Phys. 20 (1958) 948–959.

    Article  ADS  Google Scholar 

  16. R. Zwanzig, J. Chem. Phys. 33 (1960) 1338–1341.

    Article  MathSciNet  ADS  Google Scholar 

  17. S. Chaturvedi and F. Shibata, Z. Phys. B35 (1979) 297–308.

    ADS  Google Scholar 

  18. R. J. Cook, Progr. Opt. 28 (1990) 361.

    Article  Google Scholar 

  19. G. Benson, G. Raithel, H. Walther, Phys. Rev. Lett. 72 (1994) 3506.

    Article  ADS  Google Scholar 

  20. H. Carmichael, An Open Systems Approach to Quantum Optics, Lecture Notes in Physics m18 (Springer-Verlag, Berlin, 1993).

    MATH  Google Scholar 

  21. V. Gorini, A. Kossakowski, E. C. G. Sudarshan, J. Math. Phys. 17 (1976) 821–825.

    Article  ADS  MathSciNet  Google Scholar 

  22. G. Lindblad, Comm. Math. Phys. 48 (1976) 119–130.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  23. C. W. Gardiner and P. Zoller, Quantum Noise, 2nd edition (Springer-Verlag, Berlin, 2000).

    MATH  Google Scholar 

  24. R. Alicki and J. Messer, J. Stat. Phys. 32 (1983) 299–312.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  25. K. Kraus, States, Effects, and Operations (Springer-Verlag, Berlin, 1983).

    Book  MATH  Google Scholar 

  26. R. P. Feynman and F. L. Vernon, Ann. Phys. (N. Y.), 24 (1963) 118–173.

    Article  ADS  MathSciNet  Google Scholar 

  27. A. O. Caldeira and A. J. Leggett, Physica, 121A (1983) 587–616.

    ADS  Google Scholar 

  28. H. Grabert, P. Schramm and G.-L. Ingold, Phys. Rep., 168 (1988) 115–207.

    Article  ADS  MathSciNet  Google Scholar 

  29. F. Shibata, Y. Takahashi and N. Hashitume, J. Stat. Phys., 17 (1977) 171–187.

    Article  ADS  Google Scholar 

  30. S. Chaturvedi and F. Shibata, Z. Phys. B, 35 (1979) 297–308.

    Article  MathSciNet  ADS  Google Scholar 

  31. H. P. Breuer, A. Ma, F. Petruccione, Time-local master equations: influence functional and cumulant expansion, in: Quantum Computing and Quantum Bits in Mesoscopic Systems, A.J. Leggett, B. Ruggiero, and P. Silvestrini (eds), Kluwer Academic/Plenum Publishers, in press.

    Google Scholar 

  32. H.P. Breuer, B. Kappler and F. Petruccione, Phys. Rev. A, 59 (1999) 1633–1643.

    Article  ADS  Google Scholar 

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Author information

Authors and Affiliations

  1. Physikalisches Institut, Universität Freiburg, Hermann-Herder-Str. 3, 79104, Freiburg i. Br., Germany

    Heinz-Peter Breuer & Francesco Petruccione

  2. Fachbereich Physik, Carl von Ossietzky Universität, 26111, Oldenburg

    Heinz-Peter Breuer

  3. Istituto Italiano per gli Studi Filosofici, Via Monte di Dio 14, 80132, Napoli, Italy

    Francesco Petruccione

Authors
  1. Heinz-Peter Breuer
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  2. Francesco Petruccione
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Editor information

Editors and Affiliations

  1. Dipartimento di Fisica Teorica and INFN, UniversitáTrieste, Strada Costiera 11, 34014, Trieste, Italy

    Fabio Benatti  & Roberto Floreanini  & 

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Breuer, HP., Petruccione, F. (2003). Concepts and Methods in the Theory of Open Quantum Systems. In: Benatti, F., Floreanini, R. (eds) Irreversible Quantum Dynamics. Lecture Notes in Physics, vol 622. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44874-8_4

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  • DOI: https://doi.org/10.1007/3-540-44874-8_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40223-7

  • Online ISBN: 978-3-540-44874-7

  • eBook Packages: Springer Book Archive

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