Bose-Einstein condensation of a nonideal gas

Abstract

The canonical distribution with a constraint is applied to the Bogoliubov model of a nonideal Bose gas. Two approximate solutions of the variational equations for the Bose condensate density and the 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 temperatures T above and below the critical Tc, respectively. The corresponding branches of the spectrum are investigated and the specific heat CV is considered for all temperatures with the help of the derived solutions. The low-temperature behavior CV ∼ T3/2 and CV ∼ T3 due to the contributions of free boson and phonon excitations is derived. The asymptotic behavior of CV for temperatures approaching the critical temperature Tc from below and above are approximately calculated for values of the parameters ofHe4 that are in qualitative agreement with the experiment.