Destruction of Bose-Einstein condensate by strong interactions

We study exactly soluble system of trapped bosonic particles interacting by a model harmonic forces. The model allows for detailed examination of the order parameter (condensate wave function) as well as concept of the off-diagonal and diagonal order. We analyze the effect of interactions on the condensate and show that sufficiently strong interactions, attractive or repulsive, lead to destruction of the condensate. In the thermodynamic limit this destruction has a critical character. It is shown that the existence of the coherent state of bosons is related to existence of two length scales determined by one- and two-particle reduced density matrices. The condensate can exist only if the two length scales are of the same order. Interactions, both repulsive and attractive, change their relative size which may lead to destruction of coherence in the system and depletion of the condensate. We suggest that this scenario is model independent.