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arXiv 0807.1070nucl-th
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核物理中的随机矩阵与混沌

Random Matrices and Chaos in Nuclear Physics

H. A. Weidenmuller, G. E. Mitchell

备注：
54 pages, 28 figures
发表信息：
Rev.Mod.Phys.81:539-589,2009
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摘要：

本文综述了随机矩阵理论适用于核谱的证据。在类比系统的自由度很少，一个谈到混乱（更准确地说：量子混沌）在原子核随机矩阵预测时，实现。介绍了随机矩阵理论的基本概念，其次是调查现有的实验信息的光谱波动，包括讨论违反对称性或不变性的财产。讨论了球壳模型、变形壳模型和相互作用玻色子模型中的混沌。混沌的证据也来自随机矩阵合奏后的壳模型，如嵌入式两体合奏，两体随机合奏，约束合奏。所有这些证据都表明，除了强形变核的基态区域外，混沌是核谱的一种普遍性质。

英文摘要：

The authors review the evidence for the applicability of random--matrix theory to nuclear spectra. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately: quantum chaos) in nuclei whenever random--matrix predictions are fulfilled. An introduction into the basic concepts of random--matrix theory is followed by a survey over the extant experimental information on spectral fluctuations, including a discussion of the violation of a symmetry or invariance property. Chaos in nuclear models is discussed for the spherical shell model, for the deformed shell model, and for the interacting boson model. Evidence for chaos also comes from random--matrix ensembles patterned after the shell model such as the embedded two--body ensemble, the two--body random ensemble, and the constrained ensembles. All this evidence points to the fact that chaos is a generic property of nuclear spectra, except for the ground--state regions of strongly deformed nuclei.

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