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On the weak coupling limit problem

  • L. Accardi
  • A. Frigerio
  • Lu Yun Gang 
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1396)

Abstract

We show that, in the weak coupling limit, the laser model process converges in law to a quantum diffusion whose equation is explicitly obtained.

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Bibliography

  1. [1]
    Accardi, L. Quantum Markov chains. Proceedings School of Mathematical Physics, University of Camerino 1974Google Scholar
  2. [2]
    Accardi L., and Bach, A.(1988): The harmonic oscillator as quantum central limit theorem of Bernoulli processes. Prob. Th. Rel. Fields, to appearGoogle Scholar
  3. [3]
    Accardi, L., Frigerio, A., and Lewis, J.T.(1982): Publ. RIMS (Kyoto Univ.) 18, 97–133.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Accardi, L., J. Quaegebeur: The Ito algebra of quantum Gaussian fields. J.Funct.Anal. to appearGoogle Scholar
  5. [4a]
    Accardi, L., Frigerio, A., Lu Y.G.: The weak coupling limit in the finite temperature case. Proceedings 2-d Ascona Conference on Stochastic Processes and Mathematical Physics, to appearGoogle Scholar
  6. [5]
    Davies, E.B.(1974): Commun. Math. Phys. 39, 91–110.CrossRefGoogle Scholar
  7. [6]
    Davies, E.B.(1976): Quantum Theory of Open Systems, Academic Press, London and New YorkzbMATHGoogle Scholar
  8. [7]
    Davies, E. B.(1982): One-Parameter Semigroups. Academic Press, London and New YorkzbMATHGoogle Scholar
  9. [8]
    Frigerio, A.: SLN in Mathematics vol. 1303(1988), 107–127MathSciNetGoogle Scholar
  10. [9]
    Gorini, V., Kossakowski, A., and Sudarshan, E.C.G.(1976): J. Math. Phys. 17, 821–825.MathSciNetCrossRefGoogle Scholar
  11. [10]
    Haken H. Laser theory. Springer 1984Google Scholar
  12. [11]
    Hudson, R.L., and Parthasarathy, K.R.(1984a): Commun. Math Phys. 91, 301–323.MathSciNetCrossRefGoogle Scholar
  13. [11a]
    Hudson, R.L., and Lindsay, J.M.(1985b): Springer Lecture Notes in Mathematics vol. 1136, pp. 276–305.MathSciNetCrossRefGoogle Scholar
  14. [12]
    Lindblad, G.(1976): Commun. Math. Phys. 48, 119–130.MathSciNetCrossRefGoogle Scholar
  15. [13]
    Pule, J.V.(1974): Commun. Math. Phys. 38, 241–256.MathSciNetCrossRefGoogle Scholar
  16. [14]
    Spohn, H.(1980): Rev. Mod. Phys. 53, 569–615.MathSciNetCrossRefGoogle Scholar
  17. [15]
    van Hove, L.(1955): Physica 21,517–540MathSciNetCrossRefGoogle Scholar
  18. [16]
    Yoshida K. (1966): Functional Analysis. SpringerGoogle Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • L. Accardi
    • 1
  • A. Frigerio
    • 2
  • Lu Yun Gang 
    • 3
  1. 1.Centro Matematico V.Volterra Dipartimento di MatematicaUniversita' di Roma IIItaly
  2. 2.Dipartimento di Matematica e e InformaticaUniversita' di UdineItaly
  3. 3.Centro Matematico V.Volterra Dipartimento di MatematicaUniversita' di Roma IIItaly

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