快速旋转玻色-爱因斯坦凝聚体中的能量和涡度
Energy and Vorticity in Fast Rotating Bose-Einstein Condensates
摘要：
在二维Gross-Pitaevskii理论的框架下，在强耦合（Fermi）极限下，研究了有限势阱中快速旋转的玻色-爱因斯坦凝聚体.用$1/\eps^2$表示耦合参数，用$Ω$表示转动速度，用$\eps\to 0$精确地计算了参数区域$|\log\eps|\ll Ω\ll 1/(\eps^2|\log\eps|)$中次领先级对基态能量的贡献.虽然TF能量仅包括离心力的贡献，但下一阶对应于其密度与旋转速度成比例的涡旋的晶格。
英文摘要：
We study a rapidly rotating Bose-Einstein condensate confined to a finite trap in the framework of two-dimensional Gross-Pitaevskii theory in the strong coupling (Thomas-Fermi) limit. Denoting the coupling parameter by $1/\eps^2$ and the rotational velocity by $Ω$, we evaluate exactly the next to leading order contribution to the ground state energy in the parameter regime $|\log\eps|\ll Ω\ll 1/(\eps^2|\log\eps|)$ with $\eps\to 0$. While the TF energy includes only the contribution of the centrifugal forces the next order corresponds to a lattice of vortices whose density is proportional to the rotational velocity.
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