The ensemble equivalence problem for Bose systems (nonideal Bose gas)
Teoretičeskaâ i matematičeskaâ fizika, Tome 69 (1986) no. 3, pp. 420-438
V. A. Zagrebnov; V. V. Papoyan. The ensemble equivalence problem for Bose systems (nonideal Bose gas). Teoretičeskaâ i matematičeskaâ fizika, Tome 69 (1986) no. 3, pp. 420-438. http://geodesic.mathdoc.fr/item/TMF_1986_69_3_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of the equivalence of the canonical and grand canonical ensembles for nonideal Bose systems is considered for the example of three exactly solvable models, each of which undergoes a phase transition with the formation of a Bose condensate. It is shown that violation of the statistical (strong) equivalence of the ensembles is not a simple consequence of Bose condensation and equivalence is restored by changing the kind of the phase transition.

[1] Bogolyubov N. N., Lektsii po kvantovoi statistike. Izb. trudy v trekh tomakh, t. 2, Naukova dumka, K., 1970 | MR

[2] Zagrebnov V. A., Papoyan Vl. V., “Idealnyi boze-gaz: fluktuatsii i neekvivalentnost ansamblei”, III Mezhdunarodnyi simpozium po izbrannym problemam statisticheskoi mekhaniki, t. 1 (Dubna, 1984), OIYaI, Dubna, 1984, 301–309; Препринт Д17-84-850; Загребнов В. А., Папоян Вл. В., О проблеме эквивалентности ансамблей для бозе-систем (идеальный бозе-газ), Препринт Р17-85-403, ОИЯИ, Дубна, 1985 | MR

[3] Ziff R. M., Uhlenbeck G. E., Kac M., Phys. Rep., 32C:4 (1977), 169–248 | DOI | MR

[4] Khuang K., Statisticheskaya mekhanika, Mir, M., 1966; Huang K., “Imperfect Bose Gas”, Studies in Statistical Mechanics, v. II, North-Holland Publishing Comp., Amsterdam, 1964, 3–106 | MR

[5] Davies E. B., Commun. Math. Phys., 28:1 (1972), 69–86 | DOI | MR

[6] Angelescu N., Nenciu G., Tonchev N. S., On the Theory of the Excitonic Phase Transition in the Presence of a Reservoir, Preprint E17-82-798, JINR, Dubna, 1982

[7] Bogolyubov N. N. (ml.), Brankov I. G., Zagrebnov V. A., Kurbatov A. M., Tonchev N. S., Metod approksimiruyuschego gamiltoniana v statisticheskoi fizike, Izd-vo BAN, Sofiya, 1981

[8] Ryuel D., Statisticheskaya mekhanika. Strogie rezultaty, Mir, M., 1971

[9] Fannes M., Verbeure A., J. Math. Phys., 21:7 (1980), 1809–1818 | DOI | MR

[10] Buffet E., Pulé J. V., J. Math. Phys., 24:6 (1983), 1608–1616 | DOI | MR

[11] Van den Berg M., Lewis J. T., de Smedt Ph., J. Stat. Phys., 37:5/6 (1984), 697–707 | DOI | MR

[12] Minlos R. A., UMN, 23:1 (1968), 133–190 | MR

[13] Berezin F. A., Sinai Ya. G., Tr. Mosk. matem. ob-va, 17, 1967, 197–212 | MR

[14] Dobrushin R. L., “Existence of Phase Transitions in Models of a Lattice Gas”, Proc. Fifth Berkeley Symposium Math. Stat. and Prob., VI (Berkeley, 1967), 73–87

[15] Lewis J. T., Pulé J. V., de Smedt Ph., The Persistence of Boson Condensation in the Van der Waalls' Limit, Preprint DIAS-STP-85-07, Dublin, 1985 | MR

[16] Papoyan Vl. V., Zagrebnov V. A., Phys. Lett., 113A:1 (1985), 8–10 | DOI | MR