Characterization of random features of chaotic eigenfunctions in unperturbed basis
Characterization of random features of chaotic eigenfunctions in unperturbed basis
复制标题
无扰动基下混沌本征函数随机特征的表征
DOI：
10.1103/physreve.97.062219
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发表时间：
2018
影响因子：
2.4
通讯作者：
Wang Wen-ge
中科院分区：
文献类型：
--
作者：
Wang Jiaozi;Wang Wen-ge
在本文中，我们研究了量子混沌系统能量本征函数分量中表现的随机特征，这些特征是在未受扰动的可积系统的基础上给出的。基于半经典分析，特别是贝里猜想，表明当相对于特征函数的平均形状适当地重新缩放时，经典允许区域中的分量在某种意义上可以被视为高斯随机数。这表明，当扰动系统从可积变为混沌时，经典允许区域中重新缩放分量的分布与高斯分布的偏差可以用作到量子混沌的“距离”的度量。在 Lipkin-Meshkov-Glick 模型和 Dicke 模型中进行的数值模拟表明，这种偏差与随机矩阵理论预测的最近层间距分布的偏差一致。在没有经典模型的两个模型中也获得了类似的数值结果。
In this paper we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's conjecture, it is shown that the components in classically allowed regions can be regarded as Gaussian random numbers in a certain sense, when appropriately rescaled with respect to the average shape of the eigenfunctions. This suggests that when a perturbed system changes from integrable to chaotic, deviation of the distribution of rescaled components in classically allowed regions from the Gaussian distribution may be employed as a measure for the “distance” to quantum chaos. Numerical simulations performed in the Lipkin-Meshkov-Glick model and the Dicke model show that this deviation coincides with the deviation of the nearest-level-spacing distribution from the prediction of random-matrix theory. Similar numerical results are also obtained in two models without classical counterpart.