Systematic Characterization of mth‐Order Energy‐Level Spacing Distributions
Systematic Characterization of mth‐Order Energy‐Level Spacing Distributions
复制标题
米阶能级间距分布的系统表征
DOI：
10.1063/1.1704175
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发表时间：
1964
期刊：
影响因子：
--
通讯作者：
H. Leff
中科院分区：
文献类型：
--
作者：
H. Leff
根据一般的联合概率分布Pn(λ1，…)来定义复谱的m阶能级间隔分布p(M)(xλN)对于N个连续的特征值。对所涉及的精确极限过程进行了解释，并随后使用这些过程得到了p(M)(X)的两个形式表示。这两个表示都产生p(M)(X)=Xm/m！EXP(−x)表示统计独立的特征值。其中一个表示是Dyson方法在m=0，1时的推广，它被应用于n个独立的能级序列的叠加。得到了关于(A)小x，任意n和(B)任意x具有n→∞的m阶分布的一般渐近结果。
The mth‐order energy‐level spacing distributions p(m)(x) for complex spectra are defined in terms of a general joint probability distribution PN(λ1, … λN) for N consecutive eigenvalues. The precise limiting processes involved are explained, and are subsequently used to obtain two formal representations of p(m)(x). Both representations yield p(m)(x) = xm/m! exp (−x) for statistically independent eigenvalues. One of the representations, which is an extension of Dyson's method for m = 0, 1, is applied to the superposition of n independent sequences of levels. General asymptotic results are found for the mth‐order distributions for (a) small x, arbitrary n, and (b) arbitrary x with n → ∞.