A Brief Introduction to Stationary Quantum Chaos in Generic Systems

DOI10.33581/1561-4085-2020-23-2-172-191zbMath1452.81002OpenAlexW3048035108MaRDI QIDQ5145571

Marko Robnik

Publication date: 21 January 2021

Published in: Nonlinear Phenomena in Complex Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.33581/1561-4085-2020-23-2-172-191

zbMATH Keywords

Hamiltonian systemrandom matrix theoryquantum chaosspectral statisticsmixed-type classical phase space

Mathematics Subject Classification ID

Quantum chaos (81Q50) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory (81-01)

Cites Work

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• Normal modes of billiards portrayed in the stellar (or nodal) representation
• Some Generic Properties of Level Spacing Distributions of 2D Real Random Matrices
• Quantising a generic family of billiards with analytic boundaries
• Semiempirical theory of level spacing distribution beyond the Berry–Robnik regime: modeling the localization and the tunneling effects
• Semiclassical level spacings when regular and chaotic orbits coexist
• Intermediate statistics in the regime of mixed classical dynamics
• On spectral statistics of classically integrable systems
• Semiclassical energy level statistics in the transition region between integrability and chaos: transition from Brody-like to Berry-Robnik behaviour
• Statistical properties of high-lying chaotic eigenstates
• Numerical demonstration of the Berry-Robnik level spacing distribution
• The distribution of localization measures of chaotic eigenstates in the stadium billiard

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