Considering an effectively attractive quasi-one-dimensional Bose-Einstein
condensate of atoms confined in a toroidal trap, we find that the system
undergoes a phase transition from a uniform to a localized state, as the
magnitude of the coupling constant increases. Both the mean-field
approximation, as well as a diagonalization scheme are used to attack the
problem.Comment: 4 pages, 4 ps figures, RevTex, typographic errors correcte
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