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Delocalization to self-trapping transition of a Bose fluid confined in a double well potential. An analysis via one- and two-body correlation properties

We revisit the coherent or delocalized to self-trapping transition in an interacting bosonic quantum fluid confined in a double well potential, in the context of full quantum calculations. We show that an $N$-particle Bose-Hubbard fluid reaches an stationary state through the two-body interactions. These stationary states are either delocalized or self-trapped in one of the wells, the former appearing as coherent oscillations in the mean-field approximation. By studying one- and two-body properties in the energy eigenstates and in a set of coherent states, we show that the delocalized to self-trapped transition occurs as a function of the energy of the fluid, provided the interparticle interaction is above a critical or threshold value. We argue that this is a type of symmetry-breaking continuous phase transition.