Bose--Einstein condensation of nonideal gas
Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 2, pp. 295-306
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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.
@article{TMF_1996_109_2_a9,
author = {V. S. Yarunin},
title = {Bose--Einstein condensation of nonideal gas},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {295--306},
publisher = {mathdoc},
volume = {109},
number = {2},
year = {1996},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1996_109_2_a9/}
}
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/