论文标题
重新审视具有内部自由度的Calogero-Moser模型
Calogero-Moser models with internal degrees of freedom revisited
论文作者
论文摘要
我们讨论具有内部自由度的经典Calogero-Moser模型的各种示例。这些模型除了具有一些有吸引力的特性（例如完整的集成性）外，还对量子混沌系统的光谱特性很感兴趣。内部自由度的作用至少在两个方面很重要。首先，它们在动态发展的特征值之间动态发展，因此会影响特征值动力学的速度。其次，它们的初始值决定了在演变过程中可以访问的特定对之间耦合的“可触及度集”。基于扩展相位空间中线性模型的降低，以独立的方式在矩阵动力学的框架中研究了所考虑的模型。这种方法使得在各种类型的类似模型之间使用“媒介自由度”并构建类似类型的新系统。
We discuss various examples of classical Calogero-Moser models with internal degrees of freedom. These models besides of having some attractive properties, like the complete integrability, are of interest eg., in studying spectral properties of quantum chaotic systems. The role of internal degrees of freedom is important in at least two aspects. Firstly, they come in play as dynamically evolving couplings between repelling pairs of eigenvalues, hence they influence the speed of eigenvalue dynamics. Secondly their initial values determine the "reachable sets" of couplings between particular pairs accessible during the evolution. The considered models are studied in a framework of matrix dynamics in a unifed way based on a reduction of a linear model in an extended phase-space. Such an approach enables showing an equivalencies among various types of similar models employing "vectorial degrees of freedom" and constructing new systems of similar type.
