Semiclassical Mechanics, Chaos, and Phase Space Localization

在这个项目中，作者将研究混沌动力系统的量子力学和经典力学之间的对应关系。他将应用半经典近似和统计分析，如随机矩阵理论，以便将各种量子波现象与经典轨迹的性质联系起来。他将考虑一些系统，以及它们如何应对被干扰的情况，以此作为提取关于系统本身的新信息的一种方式。此外，他还将讨论如何将近似和分析扩展到受狄拉克、克莱因-戈登和/或泡利方程支配的相对论系统的基本问题。拟议的活动是高度多学科的，是一项新兴的非线性动力学科学事业。对学生在波力学和非线性动力学综合领域的培训为他们未来的各种努力做好了准备。

In this project, the author will investigate the correspondence between the quantum and classical mechanics of chaotic dynamical systems. He will apply semiclassical approximations and statistical analyses, such as random matrix theories, in order to relate various quantum wave phenomena with the properties of the classical trajectories. He will consider a number of systems and how they respond to being perturbed as a way of extracting new information about the system itself. In addition, he will address fundamental issues concerning how to extend the approximations and analyses to relativistic systems which are governed by the Dirac, Klein-Gordon, and/or Pauli equations. The proposed activity is highly multidisciplinary and lies in an emerging scientific enterprise of nonlinear dynamics. The training of students in the combined fields of wave mechanics and nonlinear dynamics prepares them for a wide variety of future endeavors.