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Quantum Chaotic Systems and Random Matrix Theory
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This article is an introductory review of random matrix theory (RMT) and its applications, with special focus on quantum chaos. Random matrices were first used by Wigner to understand the spectra of complex nuclei from a statistical perspective. Subsequently there have been novel applications to diverse areas, e.g., atomic and molecular physics, mesoscopic and nanoscopic systems, microwave cavities, econophysics, biological sciences, communication theory. This article is designed to be accessible at the graduate and post-doctoral level.
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Higher-order spacings in the superposed spectra of random matrices with comparison to spacing ratios and application to complex systems
Higher-order spacing distributions of m-superposed COE/CUE/CSE spectra are fitted to Wigner-Dyson forms, yielding tabulated modified Dyson indices β′(k,m,β), with a uniqueness conjecture tested on the quantum kicked t...
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