Wave Field Evolution, Random Media, Chaos, and Interactions

这是一个理论物理建议，涉及受随机介质约束的系统或具有混沌动力学的系统的波动力学。简单的、少自由度的系统和多体量子系统都是我们感兴趣的。作者将讨论与经典、半经典和统计方法的进步有关的基本问题，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。研究问题涉及系统如何对扰动作出反应以及动力学性质在确定灵敏度方面所起的作用。这些答案可能会影响到物理系统的广泛范围，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-电子相互作用如何有效地改变库仑封锁体制中介观导体的统计特性方面的作用。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。作者对这些领域作出了许多重要贡献。更广泛的影响：这项工作将在许多重要方面推进我们的科学知识，并使科学教育基础设施受益。它既与实验密切相关，又强调多学科研究。在所谓的量子混沌背景下开发的技术已经应用于声学、纳米物理学、核物理学、光学以及随机介质中波传播的研究等领域。反过来，新的想法又回到了量子混沌中。因此，它充当了不同研究领域交叉受精的焦点。教育在许多方面受到影响。学生们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结合一些最新的进展而得到改善。研究生助理和/或研究生在动力系统理论、统计方法、波动渐近学方面的研究训练为他们将来广泛的追求做好了准备。一个在物理学中被低估的群体的成员将被资助为博士生。最后，这一领域正在广泛的国际社会中发展。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思想的传播。

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.