Wave Field Evolution, Random Media, Chaos, and Interactions

这是一个关于随机介质系统或具有混沌动力学的系统的波动力学的理论物理建议。简单的少自由度系统和多体量子系统都令人感兴趣。作者将讨论与经典、半经典和统计方法的发展有关的基本问题，以及这些新兴方法在远程海洋声学和量子点接触中的应用。这些研究问题涉及系统如何对扰动做出反应，以及动力学的性质在决定灵敏度方面扮演着什么角色。这些答案潜在地影响了广泛的物理系统，为理解它们提供了一种新的方法。作者建议研究：i)远程海洋声学问题，ii)量子点接触附近的扫描显微镜测量，以及iii)单粒子动力学在确定电子-电子相互作用在改变库仑阻挡区介观导体统计性质方面的作用。所有这些问题都可以通过动力系统理论、半经典、统计和平均场技术协同结合来解决。作者在这些领域做出了许多重大贡献。更广泛的影响：这项工作将在许多重要方面促进我们的科学知识，并使科学教育基础设施受益。它既与实验有很强的联系，又非常重视多学科研究。在所谓的量子混沌背景下开发的技术已被应用于声学、纳米物理、核物理、光学和研究波在随机介质中的传播等。反过来，新的想法又回流到量子混沌中。因此，它充当了不同研究领域的交叉受精的焦点。教育正受到多方面的影响。学生对混沌研究表现出极大的兴趣，这有助于吸引/留住聪明的学生。他们的课堂体验通过融入一些最新的进步而得到改善。研究生助理和/或研究生在动力系统理论、统计方法、波动渐近性方面的研究培训为他们未来的广泛追求做好了准备。这笔助学金将资助物理学中代表性不足的群体的成员成为博士生。最后，这一领域正在广泛的国际社会中得到发展。对这项工作的支持导致了许多欧洲、亚洲、前苏联和南美研究人员之间的思想传播。

This is a theoretical physics proposal concerned with wave mechanics of systems subject to random media or systems possessing chaotic dynamics. Both simple, few-degree-of freedom systems and many-body quantum systems are of interest. The author will address fundamental issues related to the advancement of classical, semiclassical, and statistical methods as well as applications of such emerging methods to long range ocean acoustics and quantum point contacts. The research questions address how systems respond to perturbations and what role the nature of the dynamics plays in determining the sensitivity. The answers potentially impact a broad spectrum of physical systems providing a new approach to their understanding. The author proposes to investigate: i) long range ocean acoustics problems, ii) the scanning microscopy measurements near quantum point contacts, and iii) the role of single particle dynamics in determining how effective the electron-electron interactions are in altering the statistical properties of mesoscopic conductors in the Coulomb blockade regime. All these problems can be approached through dynamical system theory, semiclassical, statistical, and mean-field techniques that combine synergistically. The author has made a number of significant contributions to these fields. Broader Impacts: This work will advance our scientific knowledge and benefit science education infrastructure in a number of important ways. There is both a strong connection to experiments and a strong emphasis on multi-disciplinary studies. Techniques developed in the context of so-called quantum chaos have been applied in acoustics, nanophysics, nuclear physics, optics, and the study of wave propagation through random media amongst others. In turn, new ideas are flowing back into quantum chaos. As a consequence, it acts as a focal point for cross-fertilization of disparate research fields. Education is being affected in a number of ways. Students show a great deal of interest in chaos studies, and this helps attract/retain bright students. Their classroom experiences are improved by incorporating some of the latest advances. The research training of postgraduate associates and/or graduate students in dynamical systems theory, statistical methods, wave asymptotics prepares them for a wide variety of future pursuits. A member of an underrepresented group in physics will be supported as a Ph. D. student by this grant. As a final remark, this field is being developed in a broad international community. Support for this work leads to dissemination of ideas between many European, Asian, former Soviet, and South American researchers.