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date: 22 September 2019

Abstract and Keywords

This article discusses some applications of random matrix theory (RMT) to quantum or wave chaotic resonance scattering. It first provides an overview of selected topics on universal statistics of resonances and scattering observables, with emphasis on theoretical results obtained via non-perturbative methods starting from the mid-1990s. It then considers the statistical properties of scattering observables at a given fixed value of the scattering energy, taking into account the maximum entropy approach as well as quantum transport and the Selberg integral. It also examines the correlation properties of the S-matrix at different values of energy and concludes by describing other characteristics and applications of RMT to resonance scattering of waves in chaotic systems, including those relating to time delays, quantum maps and sub-unitary random matrices, and microwave cavities at finite absorption.

Keywords: random matrix theory (RMT), resonance scattering, non-perturbative method, scattering energy, maximum entropy approach, quantum transport, Selberg integral, correlation properties, S-matrix, chaotic system

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