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• W1780344488 abstract "As is well-known, statistics of highly excited bound states of closed quantum chaotic systems of quite different microscopic nature is universal. Namely, it turns out to be independent of the microscopic details when sampled on the energy intervals large in comparison with the mean level separation, but smaller than the energy scale related by the Heisenberg uncertainty principle to the relaxation time necessary for the classically chaotic system to reach equilibrium in the phase space [1]. Moreover, the spectral correlation functions turn out to be exactly those which are provided by the theory of large random matrices on the local scale determined by the typical separation between neighboring eigenvalues situated around a point X, with brackets standing for the statistical averaging [2]. Microscopic justifications of the use of random matrices for describing the universal properties of quantum chaotic systems have been provided recently by several groups, based both on traditional semiclassical periodic orbit expansions [3, 4] and on advanced field-theoretical methods [5, 6]. These facts make the theory of random Hermitian matrices a powerful and versatile tool of research in different branches of modern theoretical physics, see e.g. [2, 7].KeywordsChaotic SystemRandom MatriceComplex EigenvalueEigenvalue DensityGaussian Unitary EnsembleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
• W1780344488 created "2016-06-24" @default.
• W1780344488 creator A5011588658 @default.
• W1780344488 date "1999-01-01" @default.
• W1780344488 modified "2023-09-25" @default.
• W1780344488 title "Almost-Hermitian Random Matrices: Applications to the Theory of Quantum Chaotic Scattering and Beyond" @default.
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• W1780344488 doi "https://doi.org/10.1007/978-1-4615-4875-1_15" @default.
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