Order and Chaos in Classical and Quantum Mechanics

经典与量子力学中的秩序与混沌

• 批准号: 0457070
• 负责人: John Delos
• 金额: --
• 依托单位: College of William and Mary
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0457070&HistoricalAwards=false
• 关键词: Order; Chaos; Classical; Quantum; Mechanics

Research is proposed on semiclassical methods for calculating the behavior of quantumsystems whose classical counterparts are chaotic. The primary focus will be on breakup of anexcited complex. Of particular interest is the study of the ionization of atoms in electric andmagnetic fields. If an atom is excited by a single-photon process from a strongly bound state bya short-pulse laser, A + hv = A*, and then the excited state decays, A* = A+ + e-, it is possible tomeasure the time between the laser pulse and the appearance of an electron at a detector. Suchmeasured "time spectra" do not show exponential decay; instead, electrons appear at the detectorin a train of pulses. These pulses are related to classical orbits of the electron. Calculationsbased upon classical mechanics indicate that these chaotic pulse-trains are described by a kind offractal. We are analyzing the structure of such fractals and making predictions of results offuture experiments.In addition we will continue to apply closed-orbit theory to atomic spectra. There arenew experimental measurements in several laboratories, and we will help to provide theoreticalinterpretation of these measurements.

提出研究计算经典量子系统行为的半经典方法，而经典量子系统是混沌的。主要的焦点将放在激发复合物的分裂上。特别感兴趣的是研究原子在电场和磁场中的电离.如果一个原子被短脉冲激光从强束缚态激发出一个单光子过程，A + hv = A*，然后激发态衰减，A* = A+ + e-，那么就有可能测量出激光脉冲和电子在探测器上出现之间的时间。这种测量的“时间谱”并不显示指数衰减;相反，电子以一系列脉冲的形式出现在探测器上。这些混沌脉冲与电子的经典轨道有关，基于经典力学的计算表明，这些混沌脉冲序列可用一种分形来描述。我们正在分析这种分形的结构，并对未来的实验结果进行预测。此外，我们将继续把闭合轨道理论应用于原子光谱。在几个实验室中有新的实验测量，我们将帮助提供这些测量的理论解释。