旋转玻色-爱因斯坦凝聚体的曲柄Hartree-Fock-Bogoliubov计算
Cranked Hartree-Fock-Bogoliubov Calculation for Rotating Bose-Einstein Condensates
摘要：
本文用三维曲柄Hartree-Fock-Bogoliubov方法研究了零温下谐振势阱中的旋转玻色多体系统，该方法已应用于高自旋核多体系统。该方法是Hartree-Fock理论的一个推广，它能以自洽的方式处理对关联。这种方法的一个优点是，组成粒子之间的有限范围的相互作用可以在计算中使用，不同于原来的Gross-Pitaevskii方法。为了证明我们的方法的有效性，我们提出了一个玩具模型的计算，即一个旋转系统的十玻色子相互作用通过排斥四极-四极相互作用在一个谐波陷阱。结果表明，对于给定的总角动量，能量最低的yrast态除了少数特殊情况外，并不对应于玻色-爱因斯坦凝聚体.这种情况之一是涡旋状态，其出现在总角动量$L$是粒子数$N$的两倍时（即，$L=2N$）。
英文摘要：
A rotating bosonic many-body system in a harmonic trap is studied with the 3D-Cranked Hartree-Fock-Bogoliubov method at zero temperature, which has been applied to nuclear many-body systems at high spin. This method is a variational method extended from the Hartree-Fock theory, which can treat the pairing correlations in a self-consistent manner. An advantage of this method is that a finite-range interaction between constituent particles can be used in the calculation, unlike the original Gross-Pitaevskii approach. To demonstrate the validity of our method, we present a calculation for a toy model, that is, a rotating system of ten bosonic particles interacting through the repulsive quadrupole-quadrupole interaction in a harmonic trap. It is found that the yrast states, the lowest-energy states for the given total angular momentum, does not correspond to the Bose-Einstein condensate, except a few special cases. One of such cases is a vortex state, which appears when the total angular momentum $L$ is twice the particle number $N$ (i.e., $L=2N$).
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