Statistical Properties of Interacting Many-body Systems and other Finite Systems

这个项目关注的是介观系统的统计特性。研究了简单的少自由度系统和多体量子系统。与经典，半经典和统计方法的进步有关的基本问题得到了解决，影响了广泛的物理系统，并提供了一种新的方法来理解它们。作者建议研究：i）由于电子-电子相互作用引起的基态涨落; ii）多体相互作用系统中Kolmogorov-Sinai熵的解析近似; iii）使用Herman-Kluk传播子理解混合相空间系统中的定域特征和输运的可能性; iv）本征态极值的统计特性;以及v）经典求和规则中的涨落。这些问题是通过动力系统理论，半经典，统计和平均场技术，联合收割机协同处理。PI在这些领域做出了许多重大贡献。更广泛的影响：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，光学和多体系统的研究。反过来，新的想法又回到了量子混沌中，成为不同研究领域交叉施肥的焦点。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。他们的课堂经验包含了一些最新的进步。研究生助理和/或研究生在动力系统理论，统计方法和多体物理学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。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。

This project is concerned with the statistical properties of mesoscopic systems. Both simple, few-degree-of-freedom systems and many-body quantum systems are studied. Fundamental issues related to the advancement of classical, semiclassical, and statistical methods are addressed, impacting a broad spectrum of physical systems and providing a new approach to their understanding. The author proposes to investigate: i) ground state fluctuations due to electron-electron interactions; ii) analytic approximations to the Kolmogorov-Sinai entropy in many-body interacting systems; iii) the possibility of using the Herman-Kluk propagator in understanding localizing features and transport in systems with mixed phase spaces; iv) the statistical properties of extreme values of eigenstates; and v) fluctuations in classical sum rules. These problems are approached through dynamical system theory, semiclassical, statistical, and mean-field techniques that combine synergistically. The PI has made a number of significant contributions to these fields. Broader Impacts: 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 many-body systems. In turn, new ideas are flowing back into quantum chaos, acting as a focal point for cross-fertilization of disparate research fields. Students show a great deal of interest in chaos studies, and this helps attract/retain bright students. Their classroom experiences incorporate some of the latest advances. The research training of postgraduate associates and/or graduate students in dynamical systems theory, statistical methods, and many-body physics 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. Support for this work leads to dissemination of ideas between many European, Asian, former Soviet, and South American researchers.