Bosons in a toroidal trap: Ground state and vortices

We study the Bose-Einstein condensate (BEC) in a three-dimensional toroidal sombrero-shaped trap. By changing the parameters of the potential, or the number of bosons, it is possible to modify strongly the density profile of the BEG. We consider the ground-state properties for positive and negative scattering length and calculate the spectrum elementary excitations. We als o discuss the macroscopic phase coherence and superfluidity of the BEC by a nalyzing vortex states and their stability. [S1050-2947(99)06804-3].