Generalized Purity and Quantum Phase Transition for Bose-Einstein   condensates in a Symmetric Double Well
  The generalized purity is employed for investigating the process of coherence loss and delocalization of the Q-function in the Bloch sphere of a two-mode Bose-Einstein condensate in a symmetrical double well with cross-collision. Quantum phase transition of the model is signaled by the generalized purity as a function of an appropriate parameter of the Hamiltonian and the number of particles (N). A power law dependence of the critical parameter with N is derived. 
Thiago F. Viscondi, K. Furuya, M.C. de Oliveira