July 10, 1997 | Thomas Guhr, Axel Müller-Groeling, and Hans A. Weidenmüller
Random Matrix Theory (RMT) has seen significant development over the last decade, with applications spanning chaotic and disordered systems, many-body quantum systems, and quantum gravity. The review highlights the theoretical foundations and diverse applications of RMT, emphasizing its universality and the emergence of a new "statistical mechanics" based on stochasticity and symmetry principles. RMT was originally developed by Wigner to describe eigenvalue statistics of complex quantum systems, and has since been applied to nuclear physics, atomic and molecular systems, and quantum chaos. The theory has also found applications in disordered solids, two-dimensional quantum gravity, and chiral symmetry breaking in QCD. The review discusses the historical development of RMT and localization theory, the role of supersymmetry in RMT, and the connection between RMT and classical chaos. It also covers the application of RMT to many-body systems, quantum chaos, and disordered mesoscopic systems. The review emphasizes the universality of RMT and its ability to predict statistical properties of complex systems, despite the lack of a complete dynamical description. The paper concludes with a discussion of the broader implications of RMT, suggesting that it may represent a new kind of statistical mechanics that applies to a wide range of quantum systems.Random Matrix Theory (RMT) has seen significant development over the last decade, with applications spanning chaotic and disordered systems, many-body quantum systems, and quantum gravity. The review highlights the theoretical foundations and diverse applications of RMT, emphasizing its universality and the emergence of a new "statistical mechanics" based on stochasticity and symmetry principles. RMT was originally developed by Wigner to describe eigenvalue statistics of complex quantum systems, and has since been applied to nuclear physics, atomic and molecular systems, and quantum chaos. The theory has also found applications in disordered solids, two-dimensional quantum gravity, and chiral symmetry breaking in QCD. The review discusses the historical development of RMT and localization theory, the role of supersymmetry in RMT, and the connection between RMT and classical chaos. It also covers the application of RMT to many-body systems, quantum chaos, and disordered mesoscopic systems. The review emphasizes the universality of RMT and its ability to predict statistical properties of complex systems, despite the lack of a complete dynamical description. The paper concludes with a discussion of the broader implications of RMT, suggesting that it may represent a new kind of statistical mechanics that applies to a wide range of quantum systems.