×

zbMATH — the first resource for mathematics

Weak convergence of states in quantum statistical mechanics. (English. Russian original) Zbl 1151.82324
Dokl. Math. 76, No. 3, 958-961 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 417, No. 2, 180-184 (2007).

MSC:
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] J. von Neumann, Z. Phys. 57, 30–70 (1929).
[2] V. V. Kozlov, Gibbs and Poincaré Heat Equilibria (Izhevsk, 2002) [in Russian].
[3] J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton Univ. Press, Princeton, N.J., 1955; Nauka, Moscow, 1964).
[4] V. V. Kozlov and O. G. Smolyanov, Dokl. Math. 74, 910–913 (2006) [Dokl. Akad. Nauk 411, 587–590 (2006)]. · Zbl 1206.82054
[5] R. Alicki and M. Fannes, Quantum Dynamical Systems (Oxford Univ. Press, Oxford, 2001). · Zbl 1140.81308
[6] M. Ohia and D. Petz, Quantum Entropy and Its Use (Springer-Verlag, Berlin, 1993).
[7] A. Poincaré, in Selected Works (Nauka, Moscow, 1974), 3, pp. 385–412 [in Russian].
[8] J. E. Mayer and M. G. Mayer, Statistical Mechanics, 2nd ed. (Wiley, New York, 1977; Mir, Moscow, 1980).
[9] N. N. Bogolyubov and N. N. Bogolyubov, Jr., An Introduction to Quantum Statistical Mechanics (Nauka, Moscow, 1984) [in Russian]. · Zbl 0576.60095
[10] J. W. Gibbs, Elementary Principles in Statistical Mechanics (Yale Univ. Press, New Haven, Conn., 1902; Gostekhizdat, Moscow, 1946). · JFM 33.0708.01
[11] I. E. Farquahar, Ergodic Theory in Statistical Mechanics (London, 1964).
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.