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This review synthesizes non-perturbative random matrix methods to characterize universal statistics in open quantum and wave chaotic systems. By analyzing scattering matrices and complex resonances through an effective non-Hermitian framework, the work provides foundational insights for modeling transport in systems with finite absorption. The analysis is particularly relevant for researchers developing theoretical models where symmetry, openness, and channel coupling dictate dynamic behavior.
Random Matrix Theory for Chaotic Wave Scattering and Transport
arXiv:2606.10957v1 Announce Type: cross Abstract: We review random matrix approaches to chaotic wave scattering and transport in open systems. Starting from the effective non-Hermitian Hamiltonian formulation, we discuss the scattering matrix, reaction matrix, time delays, and complex resonances as complementary probes of open chaotic dynamics. We emphasize universal statistics governed by symmetry, openness, and channel coupling. Topics include the maximum-entropy description of fixed-energy scattering and its applications to quantum transport, energy correlations, resonance and eigenfunction statistics, and selected wave-chaotic phenomena induced by finite absorption. The focus throughout is on non-perturbative methods and universal structures underlying open quantum and wave chaotic systems.
Abstract:We review random matrix approaches to chaotic wave scattering and transport in open systems. Starting from the effective non-Hermitian Hamiltonian formulation, we discuss the scattering matrix, reaction matrix, time delays, and complex resonances as complementary probes of open chaotic dynamics. We emphasize universal statistics governed by symmetry, openness, and channel coupling. Topics include the maximum-entropy description of fixed-energy scattering and its applications to quantum transport, energy correlations, resonance and eigenfunction statistics, and selected wave-chaotic phenomena induced by finite absorption. The focus throughout is on non-perturbative methods and universal structures underlying open quantum and wave chaotic systems.
24 pages; Chapter for the Quantum Chaos volume in 'Comprehensive Quantum Physics', to be published by Elsevier (Main editor: R.B. Mann; volume editors: S. Gnutzmann and K. Życzkowski)
Chaotic Dynamics (nlin.CD); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
arXiv:2606.10957 [nlin.CD]
(or arXiv:2606.10957v1 [nlin.CD] for this version)
https://doi.org/10.48550/arXiv.2606.10957 arXiv-issued DOI via DataCite (pending registration)
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