Bose-Einstein condensates in symmetry breaking states

We consider two models of interacting Bose gases: a gas of spin one particl es in the ground state of a cubic box and a one-dimensional Bose gas with c ontact interactions. We show how to calculate exact eigenstates of the corr esponding N-body Hamiltonians. Both models share the property of not leadin g to the formation of a Bose-Einstein condensate, even at zero temperature, in the strict sense of the existence of a single one-particle state with a macroscopic population. We show that a lot of physical insight can be gain ed on these two model systems by using the usual Hartree-Fock mean field ap proach: in this approximation. that we test against the exact result. every thing happens as if a single realization of the system was a Bose-Einstein condensate in a state phi breaking the rotational or translational symmetry , and varying in a random way for any new experimental realization. (C) 200 1 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.