Geodesic
Bose–Einstein condensation of nonideal gas
Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 2, pp. 295-306 Cet article a éte moissonné depuis la source Math-Net.Ru

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The canonical distribution with a constraint is applied to the Bogoliubov model of a nonideal Bose-gas. Two approximate solutions of variational equations for the Bose-condensate density and a constraint parameter are found. They are treated as “nontrivial” and “trivial” parts of the process of Bose-condensation as far as they contribute to the thermodynamic properties at a temperature $T$ below and above the critical $T_c$ respectively. The corresponding branches of the spectrum are investigated. The heat capacity $C_V$ is considered with the help of the derived solutions for all the temperatures. Low-temperature behaviour $C_V \sim T^{3/2}$ and $C_V \sim T^3$ due to the contributions of free Boson and phonon excitations is proved. The asymptotics of $C_V$ for a temperature close to the critical temperature $T_c$ below and above it are calculated for numerical values of parameters of $\operatorname{He}^4$ in a qualitative agreement with the experiment. 
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     author = {V. S. Yarunin},
     title = {Bose{\textendash}Einstein condensation of nonideal gas},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {295--306},
     year = {1996},
     volume = {109},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_109_2_a9/}
}
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V. S. Yarunin. Bose–Einstein condensation of nonideal gas. Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 2, pp. 295-306. http://geodesic.mathdoc.fr/item/TMF_1996_109_2_a9/

[1] D. R. Tilley, J. Tilley, Superfluidity and superconductivity, Van Nostrand Company, 1974

[2] L. D. Landau, J. Phys. (USSR), 5 (1941), 71

[3] N. N. Bogolyubov, Izv. AN SSSR. Ser. fiz., 11 (1947), 77 | MR

[4] E. M. Lifshits, L. R. Pitaevskii, Statisticheskaya fizika, Nauka, M., 1978

[5] I. M. Khalatnikov, Teoriya sverkhtekuchesti, M., 1971

[6] S. T. Belyaev, ZhETF, 34 (1958), 417 | Zbl

[7] N. M. Hugenholtz, D. Pines, Phys. Rev., 116 (1962), 489 | DOI | MR

[8] V. V. Tolmachev, Teoriya boze-gaza, M., 1969

[9] V. N. Popov, L. D. Faddeev, ZhETF, 47 (1964), 1315

[10] V. N. Popov, Kontinualnye integraly v kvantovoi teorii polya i statisticheskoi fizike, Atomizdat, M., 1976 | MR

[11] D. ter Haar, Lectures on selected topics in statistical mechanics, Pergamon Press, 1977 | MR

[12] A. D. Woods, E. C. Svensson, Phys. Rev. Lett., 41 (1978), 974 | DOI

[13] H. R. Glyde, A. Griffin, Phys. Rev. Lett., 65 (1990), 1454 | DOI

[14] N. M. Blagoveshchenskii, I. V. Bogoyavlenskii, L. V. Karnatsevich, Zh. A. Kozlov, V. G. Kolobrodov, V. B. Priezzev, A. V. Puchov, A. N. Skomorokhov, V. S. Yarunin, Phys. Rev. B, 50 (1994), 16550 | DOI

[15] V. S. Yarunin, TMF, 96:1 (1993), 37

[16] V. N. Popov, V. S. Yarunin, Collective Effects in Quantum Statistics of Radiation and Matter, Kluver, Dordrecht, 1988

[17] V. S. Yarunin, L. A. Siurakshina, Physica A, 215 (1955), 261 | DOI

[18] V. I. Yukalov, Mod. Phys. Lett. B, 5 (1991), 725 | DOI | MR