Role of single-particle and pair condensates in Bose systems with arbitrary intensity of interaction

Peletminskii, Peletminskii

We study a superfluid Bose system with single-particle and pair condensates on the basis of a half-phenomenological theory of a Bose liquid not involving the weakness of interparticle interaction.The coupled equations describing the equilibrium state of such system are derived from the variational principle for entropy.These equations are analyzed at zero temperature both analytically and numerically.It is shown that the fraction of particles in the single-particle and pair condensates essentially depends on the total density of the system.At densities attainable in condensates of alkali-metal atoms, almost all particles are in the single-particle condensate.The pair condensate fraction grows with an increasing total density and becomes dominant.It is shown that at density of liquid helium, the single-particle condensate fraction is less than 10%, which agrees with experimental data on inelastic neutron scattering, Monte Carlo calculations and other theoretical predictions.The ground state energy, pressure, and compressibility are found for the system under consideration.The spectrum of single-particle excitations is also analyzed.

Joseph V. Pulé

Yu. M. Poluéktov

A self-consistent field (SCF) model is constructed for spatially inhomogeneous Bose systems with broken symmetry. A system of self-consistent equations is obtained for the wave functions of the quasiparticles and the wave function of the condensate particles and another system of equations for the normal and anomalous single-particle density matrices. The many-particle wave function is found. The thermodynamics of multiparticle Bose systems is constructed on the basis of a microscopic treatment in the SCF approximation. It is stressed that Bose condensation in the ideal gas model is substantially different from Bose condensation in a system of interacting Bose particles because a pair condensate is necessarily present as well as the single-particle condensate, even for an arbitrarily weak interaction. The role of single-particle and collective excitations in Bose systems is discussed.

Yu. M. Poluektov

G. GNANAPRAGASAM

Ernst A. Pashitskii, Stefan V. Mashkevich, S. I. Vilchynskyy

A self-consistent model of the superfluid (SF) state of a Bose liquid with strong interaction between bosons is considered, in which at T=0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC) of bosons, analogous to the Cooper pair condensate of fermions. Such a PCC emerges due to an effective attraction between bosons in some regions of momentum space, which results from an oscillating sign-changing momentum dependence of the Fourier component V(p) of the interaction potential. The collective many-body effects of renormalization ("screening") of the initial interaction, which are described by the bosonic polarization operator Π(p,ω), lead to a suppression of the repulsion [V(p)>0] and an enhancement of the effective attraction [V(p)<0] in the respective domains of nonzero momentum transfer. The ratio of the BEC density n_0 to the total particle density n of the Bose liquid is used as a small parameter of the model. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is obtained with account for the terms of first order in the BEC density. In the framework of the ``soft spheres'' model with the single fitting parameter--the value of the repulsion potential at r=0, a theoretical quasiparticle spectrum E(p) is obtained, which is in good accordance with the experimental spectrum E_{exp}(p) of elementary excitations in superfluid $^4$He.