论文标题
旋转Bose-Einstein冷凝水的基态局部唯一性与有吸引力的相互作用
Local Uniqueness of Ground States for Rotating Bose-Einstein Condensates with Attractive Interactions
论文作者
论文摘要
我们研究了二维Bose-Einstein冷凝水的基态，并在陷阱$ v（x）$上以速度$ω$旋转的陷阱相互作用。众所周知，存在关键的旋转速度$ 0 <ω^*：=ω^*（v）\ leq \ infty $和一个关键数量$ 0 <a^*<\ infty $，以至于对于任何旋转速度$ 0 \ leω<ω^*$，如果存在$ 0 \ leω<ω^*$，则仅如果存在$ a $ a $ a $ a $ a $ $ a $ a^*对于可能不是对称的陷阱$ v（x）$的一般类别，我们在本文中证明，直到一个恒定阶段，存在独特的基态，为$ a \ a \ nearrow a^*$，其中$ω\ in（0，ω^*）$是固定的。该结果基本上扩展了我们最近的唯一性结果，在该结果中只能处理径向对称的陷阱$ V（x）$。
We study ground states of two-dimensional Bose-Einstein condensates with attractive interactions in a trap $V(x)$ rotating at the velocity $Ω$. It is known that there exist a critical rotational velocity $0<Ω^*:=Ω^*(V)\leq \infty$ and a critical number $0<a^*<\infty$ such that for any rotational velocity $0\le Ω<Ω^*$, ground states exist if and only if the coupling constant $a$ satisfies $a<a^*$. 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 $a\nearrow a^*$, where $Ω\in(0,Ω^*)$ is fixed. This result extends essentially our recent uniqueness result, where only the radially symmetric traps $V(x)$ could be handled with.
