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Abstract: |
We study ground states of two-dimensional Bose-Einstein condensates with repulsive (a>0) or attractive interactions (a<0) in a trap V (x) rotating at velocityΩ. In this paper, we focus on the critical case whereΩ=Ω*to classify the existence and nonexistence of ground states. Moreover, for a suitable class of radially symmetric traps V(x), we prove that up to a constant phase, ground states must be real valued, unique, and free of vortices as Ω tends to 0, no matter whether the interactions of the condensates are repulsive or not. |
