  We investigate the thermodynamic properties of a Bose-Einstein condensate
with negative scattering length confined in a toroidal trapping potential. By
numerically solving the coupled Gross-Pitaevskii and Bogoliubov-de Gennes
equations, we study the phase transition from the uniform state to the
symmetry-breaking state characterized by a bright-soliton condensate and a
localized thermal cloud. In the localized regime three states with a finite
condensate fraction are present: the thermodynamically stable localized state,
a metastable localized state and also a metastable uniform state. Remarkably,
the presence of the stable localized state strongly increases the critical
temperature of Bose-Einstein condensation.
