RUI: Level Statistics of Continuous Energy Spectra

混沌是一个通用的术语，用来描述物理系统的不规则和不可预测的时间演化。在经典力学中，混沌可以根据附近粒子轨迹的行为来定义。由于经典力学可以被认为是量子力学的特例，人们很有兴趣知道经典混沌系统的不规则性是如何影响相应量子系统的动力学的。量子力学的标志之一是能级的量子化。现在看来，混沌在能级的分布中表现得很明显。能级分布的前提是能级是离散的。然而，如果电子几乎从原子核中剥离，能级间隔的宽度基本上为零，能量变得连续。在非束缚量子系统中也存在连续的能量，比如本项目中研究的模型，即氢原子在垂直于电场的外部磁场中。这项工作将解决如何在这个模型中寻找混沌的特征。我们计划在一个以前没有被研究过的重要能量范围内检查能级分布意义的有效性。

Chaos is the generic term used to describe the irregular and unpredictable time evolution of physical systems. In classical mechanics, chaos may be defined in terms of the behavior of nearby particle trajectories. Since classical mechanics can be thought of as a special case of quantum mechanics, it is of interest to know how the irregularity of a classically chaotic system, influences the dynamics of the corresponding quantum system. One of the trade marks of quantum mechanics is the quantization of energy levels. It now seems apparent that chaos manifests itself in the distribution of the energy levels. A distribution of energy levels presupposes that the energy levels are discrete. However, if the electron is nearly stripped from its nucleus, the widths of the energy level spacings essentially go to zero and the energies become continuous. Continuous energies are also present in unbound quantum systems like the model studied in this project, the Hydrogen atom in an external magnetic field which is perpendicular to an electric field. This work will address how one looks for signatures of chaos in this model. We plan to check the validity of the meaning of the energy level distribution in an important energy range that has not been previously investigated.