Existence and Asymptotic Behavior of Ground States for Rotating Bose–Einstein Condensates

Abstract

We study ground states of two-dimensional Bose–Einstein condensates with repulsive or attractive interactions in a trap rotating at velocity . It is known that there exist critical parameters and such that if , then there is no ground state for any ; if , then ground states exist if and only if . As a completion of the existing results, in this paper, we focus on the critical case where to classify the existence and nonexistence of ground states for any . Moreover, for a suitable class of radially symmetric traps , employing the inductive symmetry method, we prove that up to a constant phase, ground states must be real valued, unique, and free of vortices as , no matter whether the interactions of the condensates are repulsive or not.