Thermal fluctuations of the bose condensate in Bogolyubov's model of superfluidity

The method of stationary phase in the canonical ensemble with constraint is used to calculate the partition function of Bogolyubov's model from the above-condensate (quantum) and condensate (classical) variables. Expressions are obtained for the stationary values and variances of the particle numbers of both components. Numerical estimates show that the level of the thermal fluctuations of its condensate exceeds its occupation number at temperatures near the transition point, while the opposite situation holds near $0^{\mathrm{o}}$К. The significance of this circumstance for the interpretation on experiments attempting to find the density of the superfluid component in liquid $^{4}$Не is discussed.