Wave Field Evolution, Random Media, Chaos, and Interactions

点击翻译按钮获取中文摘要

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.