zbMATH — the first resource for mathematics

On Gibbs distribution for quantum systems. (English) Zbl 1253.82005
Summary: Some problems from quantum statistical mechanics concerning the regular and chaotic behavior of quantum systems are discussed.
82B05 Classical equilibrium statistical mechanics (general)
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q50 Quantum chaos
Full Text: DOI
[1] R. H. Fowler and E. A. Guggenheim, Statistical Thermodynamics (Cambridge Univ. Press, 1939).
[2] H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford Univ. Press, 2002). · Zbl 1053.81001
[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). · Zbl 1004.82002
[4] V. V. Kozlov, ”Statistical dynamics of a system of coupled pendulums,” Dokl. Math. 62(1), 129–131 (2000). · Zbl 1041.37504
[5] V. V. Kozlov, ”On justification of Gibbs distribution,” Regul. Chaotic Dyn. 7(1), 1–10 (2002). · Zbl 1019.37005
[6] V. V. Kozlov and D. V. Treschev, ”Polynomial conservation laws in quantum systems,” Theor. Math. Phys. 140(3), 1283–1298 (2004). · Zbl 1178.81158
[7] M. L. Bialy, ”On polynomial inmomenta first integrals of amechanical systemon the two-dimensional torus,” Funk. Anal. Appl. 21(4), 64–65 (1987). · Zbl 0626.43003
[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). · Zbl 0696.58022
[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). · Zbl 0964.70015
[10] A. E. Mironov, ”On polynomial integrals of a mechanical system on a two-dimensional torus,” Izvestiya: Mathematics 74(4), 805–817 (2010). · Zbl 1211.37071
[11] V. V. Kozlov, ”Thermodynamics of Hamiltonian ystems and the Gibbs istribution,” Dokl. Math. 61(1), 123–12 (2000).
[12] V. V. Kozlov, ”Topological obstructions to the integrability of natural mechanical systems,” Sov. Math. Dokl. 20, 1413–1415 (1979). · Zbl 0434.70018
[13] V. V. Kozlov, ”Topological obstructions to the existence of a quantum conservation laws,” Dokl. Math. 71(2), 300–302 (2005). · Zbl 1072.81015
[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). · Zbl 0881.58031
[15] V. V. Kozlov, Symmetries, Topology, and Resonances in Hamiltonian Mechanics (Springer-Verlag, 1996). · Zbl 0921.58029
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.