RUI: Level Statistics of Continuous Energy Spectra

RUI：连续能量谱的水平统计

• 批准号: 9601296
• 负责人: Calvin Stubbins
• 金额: $ 4.8万
• 依托单位: Franklin and Marshall College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 1998-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9601296&HistoricalAwards=false
• 关键词: RUI; Level; Statistics; Continuous; Energy

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.

混沌是用来描述物理系统的不规则和不可预测的时间演化的通用术语。 在经典力学中，混沌可以用附近粒子轨道的行为来定义。 由于经典力学可以被认为是量子力学的一个特例，因此了解经典混沌系统的不规则性如何影响相应量子系统的动力学是很有意义的。 量子力学的标志之一是能级的量子化。 现在看来很明显，混乱表现在能级的分布上。 能级的分布预先假定能级是离散的。 然而，如果电子几乎从其核中剥离，能级间距的宽度基本上为零，能量变得连续。 连续能量也存在于非束缚量子系统中，如本项目中研究的模型，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签名。 我们计划在一个重要的能量范围内，以前没有调查检查的有效性的意义的能级分布。