On the structure of the superfluid component and the spectrum of elementary excitations in the quantum Bose-liquid

A self-consistent model of superfluid (SF) Bose-liquid with a single-particle Bose-Einstein condensate (BEC) suppressed by the strong interaction between bosons is constructed. The ratio of the BEC density to the total Bose-liquid one, no/n << 1, is used as a small parameter unlike the Bogolyubov theory for almost ideal Bose-gas; the small parameter in the latter is the ratio between the number of over condensate excitations and the number of particles in the intense BEC, (n-n0)/n0 << 1. A closed set of nonlinear integral equations for normal, Σ???11(p,ω), and abnormal, Σ12(p, ω), self-energy parts is derived in terms of the renormalized perturbation theory constructed on combined hydrodynamical (for p -> 0) and field (for p ∼ 0) variables. The use of these variables ensures the analyticity of functions Σij(p, ε) for p → 0 and ε → 0 and the nonzero value or the SF order parameter Σ12(0, 0) ≠ 0 for T=0. It is shown that the spectral structure of quasi-particles, E(p), and, in particular, the existence of the roton minimum are determined by the alternating oscillating behavior of the Fourier component of the pair interaction between bosons in the 'solid sphere' model. In this case of great importance is the renormalization (<>) of the pair interaction due-to the multiparticle (collective) effects. The renormalization is described by the polarization operator of bosons on the <> and causes the effective attraction in increase in definite regions of the momentum space. It is shown that in the model under consideration the superfluid component ps at T -> 0 is a superposition of the single-particle BEC and the pair coherent condensate similar to the condensate of Cooper pairs in superconductors. The SF state structure at T not= O is considered with due account of the development of a normal component pn and a branch of the second sound, the velocity of which approaches zero at the λ-point. The points of applicability of the Landau superfluidity criterion and limiting critical velocity of the SF flow with no quantum vortices are discussed