On the Description of Quantum Dissipative Processes

  • Maurice Courbage
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 294)


The description of dissipative processes in quantum mechanics here presented is based on the existence of a time operator canonically conjugate to the Liouville operator. The entropy can be defined as a functional of this time operator and a new dissipative semi-group of time evolution can be constructed. This formalism seems well adapted to the description of the decay phenomena and the measurement process.


Liouville Operator Coherent Superposition Positivity Preserve Neumann Operator Liouville Space 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Pauli, W.: In Probleme der modernen physik, P. Debye ed. Leipzig (1928)Google Scholar
  2. [2]
    van Hove, L.: Physica 21, 362 (1955), 23, 441 (1957)Google Scholar
  3. [3]
    Prigogine, I. and Résibois, P.: Physica, 27, 629 (1961)ADSCrossRefMathSciNetGoogle Scholar
  4. [4]
    Prigogine, I.: Non equilibrium Statistical Mechanics Wiley-Inter-Science, N.Y. (1962)MATHGoogle Scholar
  5. [5]
    Balescu, R.: Equilibrium and non equilibrium Statistical Mechanics, Wiley, N.Y. (1975)Google Scholar
  6. [6]
    Résibois, P. and De Leener, M.: Classical Kinetic Theory of Fluids, Wiley, N.Y. (1977)Google Scholar
  7. [7]
    Misra, B., Prigogine, I. and Courbage, M.: Physica A 98, 1 (1979)ADSCrossRefMathSciNetGoogle Scholar
  8. [8]
    Goldstein, S., Misra, B. and Courbage, M.: J. Stat. Phys. 25, 111 (1981)ADSCrossRefMATHMathSciNetGoogle Scholar
  9. [9]
    Goldstein, S., Penrose, O.: J. Stat. Phys. 24, 325 (1981)ADSCrossRefMATHMathSciNetGoogle Scholar
  10. [10]
    Misra, B. and Prigogine, I.: Suppl. Progr. Theor. Phys. 69, 101 (1980)ADSCrossRefMathSciNetGoogle Scholar
  11. [11]
    Courbage, M.: in “Dynamical Systems and Microphysics” eds A. Avez and A. Blaquière, Academic Press, 1982Google Scholar
  12. [12]
    Misra, B.: Proc. Natl. Acad. Sci. USA, 75, 1627 (1978)ADSCrossRefGoogle Scholar
  13. [13]
    Misra, B., Prigogine, I. and Courbage, M.: Proc. Natl. Acad. Sci. USA, 76, 4768 (1979)ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    Courbage, M.: Lett. Math. Phys. 4, 425 (1980)ADSCrossRefMATHMathSciNetGoogle Scholar
  15. [15]
    Lockhart, C.M. and Misra, B.: Physica 136A, 47 (1986)CrossRefMathSciNetGoogle Scholar
  16. [16]
    Kato, T.: Perturbation theory for linear operators, Springer 1966CrossRefMATHGoogle Scholar
  17. [17]
    Reed, M. and Simon, B.: Methods of Modern Mathematical Physics I, Academic Press 1970Google Scholar
  18. [18]
    Naimark, M.A.: Normed Rings, P. Noordhoff, GroningenGoogle Scholar
  19. [19]
    Spohn, H.: J. Math. Phys. 17, 59 (1976)ADSMathSciNetGoogle Scholar
  20. [20]
    Jammer, M.: The Philosophy of Quantum Mechanics, WileyGoogle Scholar
  21. [21]
    Allcock, G.R.: Ann. Phys. (N.Y.) 53, 253 (1969)ADSCrossRefGoogle Scholar
  22. [22]
    Misra, B. and Sudarsham, E.C.G.: J. Math. Phys. 18, 756 (1977)ADSCrossRefGoogle Scholar
  23. [23]
    Courbage, M.: J. Math. Phys. 23, 646 (1982)ADSCrossRefMathSciNetGoogle Scholar
  24. [24]
    Jauch, J.M.: Helv. Phys. Acta 37, 193 (1964)MathSciNetGoogle Scholar
  25. [25]
    Hepp, J.: Helv. Phys. Acta 45, 237 (1972)Google Scholar
  26. [26]
    Takesaki, M.: J. Functional Anal. 9, 306 (1972)CrossRefMATHMathSciNetGoogle Scholar
  27. [27]
    Emch, G.G.: Com. Math. Phys. 49, 191 (1976)ADSCrossRefMATHMathSciNetGoogle Scholar
  28. [28]
    Bell, J.S.: Helv. Phys. Acta 48, 93 (1975)MATHMathSciNetGoogle Scholar
  29. [29]
    Misra, B. and Prigogine, I.: In “Long Time Prediction in Dynamics” Eds. C.W. Horton, Jr., L.E. Reichl, A.G. Szebehely, Wiley, 1983Google Scholar
  30. [30]
    Courbage, M. and Prigogine, I.: Proc. Natl. Acad. Sci. USA 80, 2412 (1980), and Courbage, M.: Physica 122A, 459 (1983)ADSCrossRefMathSciNetGoogle Scholar
  31. [31]
    Martinez, S. and Tirapegui, E.: J. Stat. Phys. 25, 111 (1981)CrossRefGoogle Scholar
  32. [32]
    Misra, B. and Prigogine, I.: Lett. Math. Phys. 7, 421 (1983)ADSCrossRefMathSciNetGoogle Scholar
  33. [33]
    Prigogine, I. and George, C.: Proc. Natl. Acad. Sci. USA, 80, 4590 (1983)ADSCrossRefMATHMathSciNetGoogle Scholar
  34. [34]
    Davies, E.B.: Quantum Theory of Open Systems, Academic Press, N.Y. (1976), Theorem 3.1, p. 21.MATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1987

Authors and Affiliations

  • Maurice Courbage
    • 1
  1. 1.Laboratoire de ProbabilitésParis CedexFrance

Personalised recommendations