Spatial fragmentation of a Bose-Einstein condensate in a double-well   potential
  We present a theoretical study of the ground state of a Bose-Einstein condensate with repulsive inter-particle interactions in a double-well potential, using a restricted variational principle. Within such an approach, there is a transition from a single condensate to a fragmented condensate as the strength of the central barrier of the potential is increased. We determine the nature of this transition through approximate analytic as well as numerical solutions of our model in the regime where the inter-particle interactions can be treated perturbatively. The degree of fragmentation of the condensate is characterized by the degrees of first-order and second-order spatial coherence across the barrier. 
R. W. Spekkens and J. E. Sipe