Action correlations and random matrix theory
Action correlations and random matrix theory
复制标题
动作相关性和随机矩阵理论
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
Basile Verdene
中科院分区：
文献类型：
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作者：
U. Smilansky;Basile Verdene
量子系统谱中的关联与真正经典起源的关联密切相关，这些关联出现在相应经典系统的经典周期轨道的作用谱中。我们回顾这种对偶性和半经典理论，使它。量子谱统计可以用随机矩阵理论描述的猜想，引出了经典两点关联函数也可以用普适函数给出的命题。我们详细研究了贝克映射的作用谱，并用它来说明揭示经典相关性所需的步骤，它们的起源及其与符号动力学的关系。
The correlations in the spectra of quantum systems are intimately related to correlations which are of genuine classical origin, and which appear in the spectra of actions of the classical periodic orbits of the corresponding classical systems. We review this duality and the semiclassical theory which brings it about. The conjecture that the quantum spectral statistics are described in terms of random matrix theory, leads to the proposition that the classical two-point correlation function is also given in terms of a universal function. We study in detail the spectrum of actions of the Baker map, and use it to illustrate the steps needed to reveal the classical correlations, their origin and their relation to symbolic dynamics.