共振BEC的超球LOCV逼近
Hyperspherical-LOCV Approximation to Resonant BEC
摘要：
我们研究了$N$系统的基态性质的谐波捕获玻色子的质量$m$相互作用与两体接触的相互作用，从小到大的散射长度。这是在一个超球面坐标系中完成的，该坐标系足够灵活，可以描述气体和两体相关性的整体尺度。通过采用最低阶约束变分方法，我们能够半定量地得到玻色-爱因斯坦凝聚体的基态能量，即使是对于具有无限散射长度的气体。在大粒子数的限制，我们的方法提供了分析估计的能量每粒子$E_0/N \approx 2.5 N^{1/3} \hbar ω$和两体接触$C_2/N \approx 16 N^{1/6}\sqrt{mω/\hbar}$的玻色气体共振，其中$ω$是陷阱频率。
英文摘要：
We study the ground state properties of a system of $N$ harmonically trapped bosons of mass $m$ interacting with two-body contact interactions, from small to large scattering lengths. This is accomplished in a hyperspherical coordinate system that is flexible enough to describe both the overall scale of the gas and two-body correlations. By adapting the lowest-order constrained variational (LOCV) method, we are able to semi-quantitatively attain Bose-Einstein condensate ground state energies even for gases with infinite scattering length. In the large particle number limit, our method provides analytical estimates for the energy per particle $E_0/N \approx 2.5 N^{1/3} \hbar ω$ and two-body contact $C_2/N \approx 16 N^{1/6}\sqrt{mω/\hbar}$ for a Bose gas on resonance, where $ω$ is the trap frequency.
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