Calculation of nonequilibrium thermodynamic potential of Bose system near the condensation point

Abstract

Bose system of zero spin particles is considered in the presence of the Bose–Einstein condensate in the vicinity of the phase transition point. The system is investigated in the framework of the Bogolyubov model with the separated condensate. In this model an effective Hamiltonian of the system is introduced by replacing condensate creation and annihilation operators in system Hamiltonian by n₀^1/2 where n₀ is occupation number of the condensate state. According to Bogolyubov, the grand canonical thermodynamic potential related to the effective Hamiltonian is considered as nonequilibrium thermodynamic potential. In the present paper this potential is investigated as a function of the small variable n0. With the help of the thermodynamic perturbation theory it is shown that it is expanded in a series over integer powers of n0. This corresponds to the basic idea of the Landau theory of the phase transitions of the second kind. Coefficients at terms of the first and second orders in n₀ in the expansion are calculated for Bose gas in the main approximation in small interaction. Calculation of the coefficients at terms of the third and fourth orders needs accounting contributions of the thermodynamic perturbation theory at least of the 4th order and will be done elsewhere. It is established that the results obtained for Bose gas do not fit into the Landau theory of phase transitions of the second kind. Some comments that discuss the situation are given.