Local Uniqueness of Ground States for Rotating Bose-Einstein Condensates with Attractive Interactions

Abstract

We study ground states of two-dimensional Bose-Einstein condensates with attractive interactions in a trap $V(x)$ rotating at the velocity $\Omega$. It is known that there exist a critical rotational velocity $0<{\Omega }^{\ast }:={\Omega }^{\ast }(V)\le \infty$ and a critical number $0<a^{\ast }<\infty$ such that for any rotational velocity $0\le \Omega <{\Omega }^{\ast }$, ground states exist if and only if the coupling constant $a$ satisfies $a<a^{\ast }$. For a general class of traps $V(x)$, which may not be symmetric, we prove in this paper that up to a constant phase, there exists a unique ground state as $a\nearrow a^{\ast }$, where $\Omega \in (0,{\Omega }^{\ast })$ is fixed. This result extends essentially our recent uniqueness result, where only the radially symmetric traps $V(x)$ could be handled with.

arXiv comment25 pages, any comments are welcome

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Cited by in corpus (2)

• The Nonexistence of Vortices for Rotating Bose-Einstein Condensates in Non-Radially Symmetric Traps
• Existence and Asymptotic Behavior of Ground States for Rotating Bose-Einstein Condensates