Wave Field Evolution, Random Media, Chaos, and Interactions

波场演化、随机介质、混沌和相互作用

• 批准号: 0555301
• 负责人: Steven Tomsovic
• 金额: $ 19.55万
• 依托单位: Washington State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0555301&HistoricalAwards=false
• 关键词: Wave; Field; Evolution; Random; Media

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.

这是一个理论物理学的建议，涉及系统的波动力学的随机介质或系统具有混沌动力学。简单的少自由度系统和多体量子系统都是感兴趣的。作者将解决与经典，半经典和统计方法的进步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有关的基本问题。研究问题解决系统如何响应扰动和动态的性质在确定灵敏度中起什么作用。这些答案可能会影响广泛的物理系统，为理解它们提供了新的方法。作者建议调查：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，和iii）单粒子动力学的作用，在确定如何有效的电子-电子相互作用是在改变统计性质的介观导体在库仑阻塞制度。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，联合收割机协同处理。作者在这些领域做出了许多重要贡献。更广泛的影响：这项工作将推进我们的科学知识，并在许多重要方面有利于科学教育基础设施。既有一个强大的连接到实验和多学科研究的强烈强调。在所谓的量子混沌背景下开发的技术已应用于声学，纳米物理学，核物理学，光学以及通过随机介质的波传播研究等领域。反过来，新的想法又回到了量子混沌中。因此，它是不同研究领域相互交流的焦点。教育正受到多方面的影响。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，波渐近的研究培训为他们准备了各种各样的未来追求。一个在物理学中代表性不足的群体的成员将被支持为博士。学生通过这种方式。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许多欧洲，亚洲，前苏联和南美研究人员之间的思想传播。