A system with Bose-Einstein condensate is considered in the frame of the self-consistent mean-field approximation, which is conserving, gapless, and applicable for arbitrary interaction strengths and temperatures. The main attention is paid to the thorough analysis of the condensate and superfluid fractions in the whole range of the interaction strength, between zero and infinity, and for all temperatures between zero and the critical point
Tc. The normal and the anomalous averages are shown to be of the same order for almost all interactions and temperatures, except the close vicinity of
Tc. But even in the vicinity of the critical temperature, the anomalous average cannot be neglected, since only in the presence of the latter the phase transition at
Tc becomes of second order, as it should be. Increasing temperature influences the condensate and superfluid fractions in a similar way, by diminishing them; but their behavior with respect to the interaction strength is very different. For all temperatures, the superfluid fraction is larger than the condensate fraction. These coincide only at
Tc or under zero interactions. For asymptotically strong interactions, the condensate is almost completely depleted, even at low temperatures, while the superfluid fraction can be close to one.
We report the effects of interaction on thermodynamic properties of a repulsive Bose-Einstein condensate confined in a harmonic trap by using the correlated potential harmonics expansion method. This many-body technique permits the use of a realistic interactomic interaction, which gives rise to the effective long-range interaction of the condensate in terms of the
s-wave scattering length. We have computed temperature (
T) dependence of the chemical potential, specific heat, condensate fraction, entropy, pressure, and the average energy per particle of a system containing a large number (
A) of
87Rb atoms in the Joint Institute for Laboratory Astrophysics (JILA) trap. The repulsion among the interacting bosons results in a small but measurable drop of condensate fraction and critical temperature (
Tc), compared to those of a noninteracting condensate. These are in agreement with the experiment. Although all thermodynamic quantities have a strong dependence on
A and to a smaller extent on the interatomic interaction, our numerical calculation appears to show that a thermodynamic quantity per particle follows a universal behavior as a function of
T/Tc. This shows the importance of
Tc for all thermodynamic properties of the condensate. As expected, for
T>Tc, these properties follow those of a trapped noncondensed Bose gas.