量子混沌与能级动力学
Quantum chaos and level dynamics
摘要：
本文综述了能级动力学在量子混沌系统谱研究中的应用。我们表明，统计力学的方法给我们的预测之间的可积和混沌动力学的中间水平统计。然后，我们详细讨论了不同的统计措施，涉及水平动力学，如水平避免交叉分布，斜率和曲率的水平分布显示的假设的unversality及其局限性。我们将简要地提到这些理论的实验证实。我们集中在一些细节的措施进口量子信息的方法，如保真度磁化率和更一般的几何张量矩阵元素。提出了可能存在的问题。
英文摘要：
We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss in detail different statistical measures involving level dynamics such as level avoided-crossing distributions, slope and curvature of level distributions showing both the postulate of unversality and its limitations. We mention shortly the experimental confirmations of these theories. We concentrate in some detail on measures imported from quantum information approach such as the fidelity susceptibility and more generally geometric tensor matrix elements. The possible open problems are suggested.
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