嵌入随机矩阵系综中的有序水平间距分布
Ordered Level Spacing Distribution in Embedded Random Matrix Ensembles
摘要：
本文研究了由一加随机二体相互作用的嵌入GOE构造的有自旋自由度和无自旋自由度的相互作用费米子/玻色子系统的最近邻和远邻距的概率分布。我们的数值结果表明，最近推导出的解析表达式，使用$3 \times 3$随机矩阵模型和其他相关的Srivastava等量的一个非常好的一致性。[{ \it J. Phys. A：Math. Theor.} { \bf 52} 025101（2019）]。这最终确定了嵌入式系综（EE）产生的局部水平波动遵循经典高斯系综的结果。
英文摘要：
The probability distribution of the closest neighbor and farther neighbor spacings from a given level have been studied for interacting fermion/boson systems with and without spin degree of freedom constructed using an embedded GOE of one plus random two-body interactions. Our numerical results demonstrate a very good consistency with the recently derived analytical expressions using a $3 \times 3$ random matrix model and other related quantities by Srivastava et. al [{\it J. Phys. A: Math. Theor.} {\bf 52} 025101 (2019)]. This establishes conclusively that local level fluctuations generated by embedded ensembles (EE) follow the results of classical Gaussian ensembles.
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