具有吸引相互作用的旋转玻色-爱因斯坦凝聚体基态的局域唯一性
Local Uniqueness of Ground States for Rotating Bose-Einstein Condensates with Attractive Interactions
摘要：
研究了以$Ω$为旋转速度的$V(x)$阱中具有吸引相互作用的二维玻色-爱因斯坦凝聚的基态.已知存在临界转速$0<Ω^*:=Ω^*(V)\leq \infty$和临界数$0<a^*<\infty$，使得对于任何转速$0\le Ω<Ω^*$，基态存在当且仅当耦合常数$a$满足$a<a^*$。对于一般的陷阱$V(x)$，这可能是不对称的，本文证明，直到一个恒定的相位，存在一个独特的基态$a\nearrow a^*$，其中$Ω\in(0,Ω^*)$是固定的。这个结果基本上扩展了我们最近的唯一性结果，其中只有径向对称的陷阱$V(x)$可以处理。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
