On Gibbs distribution for quantum systems

  • V. V. Kozlov
Research Articles


Some problems from quantum statistical mechanics concerning the regular and chaotic behavior of quantum systems are discussed.

Key words

quantum statistical mechanics regular and chaotic dynamics quantum systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. H. Fowler and E. A. Guggenheim, Statistical Thermodynamics (Cambridge Univ. Press, 1939).Google Scholar
  2. 2.
    H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford Univ. Press, 2002).Google Scholar
  3. 3.
    V. V. Kozlov, “Canonical Gibbs istribution and thermodynamics of mechanical systems with a finite number of degrees of reedom,” Regul. Chaotic Dyn. 4(2), 44–54 (1999).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    V. V. Kozlov, “Statistical dynamics of a system of coupled pendulums,” Dokl. Math. 62(1), 129–131 (2000).Google Scholar
  5. 5.
    V. V. Kozlov, “On justification of Gibbs distribution,” Regul. Chaotic Dyn. 7(1), 1–10 (2002).MathSciNetCrossRefGoogle Scholar
  6. 6.
    V. V. Kozlov and D. V. Treschev, “Polynomial conservation laws in quantum systems,” Theor. Math. Phys. 140(3), 1283–1298 (2004).zbMATHCrossRefGoogle Scholar
  7. 7.
    M. L. Bialy, “On polynomial inmomenta first integrals of amechanical systemon the two-dimensional torus,” Funk. Anal. Appl. 21(4), 64–65 (1987).MathSciNetGoogle Scholar
  8. 8.
    V. V. Kozlov and D. V. Treschev, “On the integrability of Hamiltonian systems with toral position space,” Math. USSR-Sb. 63(1), 121–139 (1989).MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    N. V. Denisova and V. V. Kozlov, “Polynomial integrals of reversible mechanical systems with a twodimensional torus as the configuration space,” Sb. Math. 191(2), 189–208 (2000).MathSciNetCrossRefGoogle Scholar
  10. 10.
    A. E. Mironov, “On polynomial integrals of a mechanical system on a two-dimensional torus,” Izvestiya: Mathematics 74(4), 805–817 (2010).MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    V. V. Kozlov, “Thermodynamics of Hamiltonian ystems and the Gibbs istribution,” Dokl. Math. 61(1), 123–12 (2000).Google Scholar
  12. 12.
    V. V. Kozlov, “Topological obstructions to the integrability of natural mechanical systems,” Sov. Math. Dokl. 20, 1413–1415 (1979).zbMATHGoogle Scholar
  13. 13.
    V. V. Kozlov, “Topological obstructions to the existence of a quantum conservation laws,” Dokl. Math. 71(2), 300–302 (2005).Google Scholar
  14. 14.
    A. V. Bolsinov, V. V. Kozlov and A. T. Fomenko, “The Maupertis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body,” RussianMath. Surveys 50(3), 473–501 (1995).MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    V. V. Kozlov, Symmetries, Topology, and Resonances in Hamiltonian Mechanics (Springer-Verlag, 1996).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

Personalised recommendations