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A continuous configuration-interaction (CCI) approach for condensates in a ring is introduced. In its simplest form this approach utilizes for attractive condensates the Gross-Pitaevskii (GP) symmetry-broken solution and arrives at a ground-state of correct symmetry. The energy found is already lower than the GP one and, with increasing number of particles and/or strength of inter-particle interaction, is even lower than that accessed by tractable diagonalization of the many-body Hamiltonian.
Furthermore, we note that any exact eigenstate with a definite angular momentum of the many-body Hamiltonian can be written as an integral over a symmetry-broken function Φ. For two bosons, we solve the problem exactly for any inter-particle interaction. Especially for the ground-state, Φ is given by the simple Hartree ansatz. For more bosons, the numerical solution of the resulting CCI equation for attractive and repulsive condensates in a ring will be preseted and discussed. |