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The generalized purity is employed for investigating the process of coherenceloss and delocalization of the Q-function in the Bloch sphere of a two-modeBose-Einstein condensate in a symmetrical double well with cross-collision.Quantum phase transition of the model is signaled by the generalized purity asa function of an appropriate parameter of the Hamiltonian and the number ofparticles (N). A power law dependence of the critical parameter with N isderived.

Generalized Purity and Quantum Phase Transition for Bose-Einstein condensates in a Symmetric Double Well