范德华集团在幺正区附近的结构和量子特性
Structural and quantum properties of van der Waals cluster near the unitary regime
摘要：
研究了大散射长度下三维玻色团簇通过范德华势相互作用的结构和几种量子性质。我们使用Faddeev型分解的多体波函数，其中包括所有可能的两体相关。在大的散射长度，我们观察到的空间扩展状态，表现出指数依赖于状态数。团簇的基态能量在负散射长度较大时具有普适性。我们还发现了$N$ -体团簇的广义Tjon线的存在性。在超冷玻色气体的实验中可以观察到弱束缚团簇普遍行为的特征。我们还研究了系统的谱统计特性。我们计算了短程涨落和长程相关，并观察到半Poisson分布，它插值于随机矩阵理论的高斯正交包络（GOE）和Poisson统计。这表明在幺正附近的范德瓦尔团簇变得高度复杂和相关。然而，对$P(r)$分布的进一步研究（没有展开能谱）揭示了较大团簇混沌的可能性。
英文摘要：
We study the structural and several quantum properties of three-dimensional bosonic cluster interacting through van der Waals potential at large scattering length. We use Faddeev-type decomposition of the many-body wave function which includes all possible two-body correlations. At large scattering length, we observe spatially extended states which exhibit the exponential dependence on the state number. The cluster ground state energy shows universal nature at large negative scattering length. We also find the existence of generalized Tjon lines for $N$- body clusters. Signature of universal behaviour of weakly bound clusters can be observed in experiments of ultracold Bose gases. We also study the spectral statistics of the system. We calculate both the short-range fluctuation and long-range.correlation and observe semi-Poisson distribution which interpolates the Gaussian Orthogonal Ensemble (GOE) and Poisson statistics of random matrix theory. It indicates that the van der Waal cluster near the unitary becomes highly complex and correlated. However additional study of $P(r)$ distribution (without unfolding of energy spectrum) reveals the possibility of chaos for larger cluster.
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