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Non-Equilibrium Quantum Statistical Mechanics

  • G. G. Emch
Part of the Few-Body Systems book series (FEWBODY, volume 15/1976)

Abstract

Through the study of a particular model, the aim of these lectures is to indicate how the so-called “algebraic approach” can help understanding the statistical mechanics of quantum stochastic transport processes.

Keywords

Quantum Particle Ergodic Property Dynamical Entropy Faithful Normal State Quantum Realm 
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.
    R. Kubo, Statistical Mechanical Theory of Irreversible Processes, I.J.Phys. Soc. Japan 12, 570–586 (1957).MathSciNetCrossRefGoogle Scholar
  2. 2.
    P.C. Martin and J. Schwinger, Theory of Many-Particle Systems, I. Phys. Rev. 115, 1342–1373 (1959).MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    R. Haag, N. Hugenholtz and M. Winnink, On the Equilibr-ium States in Quantum Statistical Mechanics, Commun, math. Phys. 16, 81–104 (1967).Google Scholar
  4. 4.
    R. Haag, D. Kastler and E. Trych-Pohlmeyer, Stability and Equilibrium States. Commun, math. Phys. 38, 173–193 (1974).MathSciNetGoogle Scholar
  5. 5.
    G.G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley-Interscience, New York, 1972 .Google Scholar
  6. 6.
    M. Takesaki, Tomita’s Theory of Modular Hilbert Algebras and its Applications, Springer Lecture Notes in Mathematics No. 128, 1970.Google Scholar
  7. 7.
    A. Connes, Une classification des facteurs de type III, Ann. scient. Ec. Norm. Sup. (4e série) 6, 133–252 (1973).MathSciNetMATHGoogle Scholar
  8. 8.
    G.W. Ford, M. Kac and P. Mazur, Statistical Mechanics of Assemblies of Coupled Oscillators, Journ. Math. Phys. 6, 504–515 (1965).MathSciNetADSMATHCrossRefGoogle Scholar
  9. 9.
    E.B. Davies, Diffusion for Weakly Coupled Quantum Oscillators, Comm. math. Phys. 27, 309–325 (1972).Google Scholar
  10. 10.
    W.F. Stinespring, Positive Functions on C*-algebras, Proc. Amer. Math. Soc. 6, 211–216 (1955).MathSciNetMATHGoogle Scholar
  11. 11.
    D.E. Evans, Positive Linear Maps on Operator Algebras. Preprint, DIAS-TP-75-39.Google Scholar
  12. 12.
    F. Riesz and B. Sz.-Nagy, Leçons d1analyse fonctionnelle Gauthier-Villars, Paris, 1955.Google Scholar
  13. 13.
    G. G. Emch, Generalized K-Flows, In preparation. This paper extends the work done in [14], [15], and [16] for summaries see [17] and [18].Google Scholar
  14. 14.
    G.G. Emch, Nonabelian Special K-flows, Journ. Funct. Analysis 19, 1–12 (1975); Zentralblattf. Math. 501130 (1975).Google Scholar
  15. 15.
    G. G. Emch, The Minimal K-Flow associated to a Quantum Diffusion Process. In Physical Reality and Mathematical Description, Ch. Enz & J. Mehra, Eds., Reidel Publ., Dordrecht, 1974, 477–493.CrossRefGoogle Scholar
  16. 16.
    G.G. Emch, Positivity of the K-entropy on Non-Abelian K-Flows, Z. Wahrscheinlichkeitstheorie verw. Gebiete 29, 241–252 (1974).MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    G.G. Emch, An Algebraic Approach to the Theory of K-Flows and K-Entropy, In Proc. Intern. Symp. on Math. Problems in Theor. Phys. Springer Lecture Notes in Physics No. 39, 1975, 315–318.MathSciNetADSGoogle Scholar
  18. 18.
    G.G. Emch, Algebraic K-Flows, In Proc. Intern. Conf. on Dynamical Systems in Math. Physics, Rennes, 1975.Google Scholar
  19. 19.
    M. Takesaki, The Structure of a v. N. Algebra with Homogeneous Periodic State. Acta Math. 131, 79–121 (1973).MathSciNetMATHGoogle Scholar
  20. 20.
    V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics, Benjamin, New York, 1968.Google Scholar
  21. 21.
    W. A. Parry, Entropy and Generators in Ergodic Theory. Benjamin, New York, 1969.Google Scholar
  22. 22.
    D.S. Ornstein, Ergodic Theory, Randomness, and Dynamical Systems, Yale University Press, New Haven, 1974.MATHGoogle Scholar
  23. 23.
    I. Kovacs and J. Szücs, Ergodic Type Theorems in von Neumann algebras. Acta Sc.Math.(Szeged)27,233–246 (1966) .Google Scholar
  24. 24.
    P. D. Lax and R.S. Phillips, Scattering Theory, Academic Press, New York, 1967.MATHGoogle Scholar
  25. 25.
    A. Khinchin, Mathematical Foundations of Information Theory, Dover, New York, 1957.MATHGoogle Scholar
  26. 26.
    A. Connes and E. Størmer, Entropy for automorphisms of II1 von Neumann algebras. Acta Math.Google Scholar
  27. 27.
    T. Hida, Stationary Stochastic Processes, Princeton University Press, Princeton, 1970.MATHGoogle Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • G. G. Emch
    • 1
  1. 1.ZiFUniversität BielefeldDeutschland

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