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

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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.