Study of the temperature dependence of single-particle and pair coherent condensate densities for a Bose liquid with a "depleted" single-particle Bose-Einstein condensate (BEC) at $T \neq 0

We study the temperature dependence of single-particle and pair coherent condensate densities for a Bose liquid with a "depleted" single-particle Bose-Einstein condensate (BEC) at $T \neq 0$. Our investigations were based on the field-theoretical Green's functions. On the basis of the use of empirical data about the speeds of the first and second sounds is described superfluid state at $T \neq 0$. It is studied the structure of superfluid state taking into account appearance with the different from zero temperatures of normal component and taking into account the branch of the second sound, whose speed approaches zero at $T \to T_\lambda$. The bare interaction between bosons was chosen in the form of a repulsive Azis potential, the Fourier component of which was an oscillatory and sign-varying function of the momentum. The obtained temperature dependence of single-particle and pair coherent condensate and total densities has a good agreement with experiment data.