Condensate and superfluid fractions for varying interactions and temperature

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 a wide region of interaction strengths and for all temperatures between zero and the critical point T_c. The normal and anomalous averages are shown to be of the same order for almost all interactions and temperatures, except the close vicinity of T_c. 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 T_c 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 T_c 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.