旋转非谐势阱中玻色-爱因斯坦凝聚体的巨涡旋态：极端旋转区
The giant vortex state for a Bose-Einstein condensate in a rotating anharmonic trap : extreme rotation regimes
摘要：
在二维Gross-Pitaevskii能量泛函的框架下，研究了二次加四次约束势中玻色-爱因斯坦凝聚体的快转极限。由于旋转速度趋于无穷大，在模型中的其他参数的适当缩放，线性极限问题出现，我们能够得到精确的能量估计。我们证明了问题的能量和密度渐近性可以通过极小化一个简化的一维能量泛函得到。在固定耦合常数的情况下，我们还证明了巨涡旋态的出现。它是一个具有纯无旋流动的环，环绕着中心低密度孔，周围有宏观相循环。
英文摘要：
We study the fast rotation limit for a Bose-Einstein condensate in a quadratic plus quartic confining potential within the framework of the two dimensional Gross-Pitaevskii energy functional. As the rotation speed tends to infinity with a proper scaling of the other parameters in the model, a linear limit problem appears for which we are able to derive precise energy estimates. We prove that the energy and density asymptotics of the problem can be obtained by minimizing a simplified one dimensional energy functional. In the case of a fixed coupling constant we also prove that a giant vortex state appears. It is an annulus with pure irrotational flow encircling a central low-density hole around which there is a macroscopic phase circulation.
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