$Δ_3$统计量的遍历性和中子共振数据的纯度
Ergodicity of the $Δ_3$ statistic and purity of neutron resonance data
摘要：
$Δ_3(L)$统计量表征了作为谱间隔长度的函数的能级数目的波动。它被研究作为一种可能的工具，以指示潜在的动力学的规则或混沌的性质，检测丢失的水平和不同对称性的水平的序列的混合，特别是在中子共振数据。被认为是一个给定的实现光谱的不同片段的系综平均和平均之间的关系。讨论了有限样本下$Δ_3(L)$方差的一个有用表达式。中子共振数据的分析结果与应用于能级间距分布的极大似然方法一致。
英文摘要：
The $Δ_3(L)$ statistic characterizes the fluctuations of the number of levels as a function of the length of the spectral interval. It is studied as a possible tool to indicate the regular or chaotic nature of underlying dynamics, detect missing levels and the mixing of sequences of levels of different symmetry, particularly in neutron resonance data. The relation between the ensemble average and the average over different fragments of a given realization of spectra is considered. A useful expression for the variance of $Δ_3(L)$ which accounts for finite sample size is discussed. An analysis of neutron resonance data presents the results consistent with a maximum likelihood method applied to the level spacing distribution.
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