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

这个项目是关于介观系统的统计性质。研究了简单的、少自由度的系统和多体量子系统。与经典、半经典和统计方法的进步相关的基本问题得到了解决，影响了物理系统的广泛范围，并提供了一种新的理解方法。作者建议研究：i)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)利用Herman-Kluk传播子来理解混合相空间系统中的局部特征和输运的可能性；Iv)特征态极值的统计性质；v)经典求和规则的波动。这些问题是通过动力系统理论、半经典、统计和平均场技术协同结合来解决的。PI在这些领域做出了许多重大贡献。更广泛的影响：与实验有很强的联系，并且非常强调多学科研究。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、光学和多体系统的研究。反过来，新的想法又回流到量子混沌中，成为不同研究领域交叉受精的焦点。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。他们的课堂体验融合了一些最新的进展。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方面的研究训练为他们将来广泛的追求做准备。一个在物理学中被低估的群体的成员将被资助为博士生。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 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.