Didactic derivation of Gutzwiller's trace formula from the path integral, with overview of its use in explaining random matrix theory statistics for quantum energy levels.
Hamiltonian Chaos
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Through semiclassical methods the subject of quantum chaos motivates and depends on Hamiltonian chaos research. Presented here is a selection of Hamiltonian chaos topics that in this way get directly related to any of a variety of quantum chaos research problems. The chapter begins with a description of various useful theoretical and computational tools of chaos research, e.g.~surfaces of section, paradigms of chaos, stability analysis, and symbolic dynamics... This is followed by discussions regarding the geometry of chaos, how chaotic systems respond to perturbations, and the complexification of Hamiltonian dynamics. The emphasis is on intuitive explanations and illustrations of various ideas with the references containing more mathematically rigorous expositions.
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quant-ph 3years
2026 3verdicts
UNVERDICTED 3roles
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Quantum graphs are presented as a paradigmatic model for quantum chaos, with the paper providing a didactical overview of foundational results and some recent developments.
Review of random matrix theory application to quantum chaos, covering symmetry classes, eigenvalue statistics, unfolding, and correlation functions.
citing papers explorer
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Semiclassical periodic-orbit theory for quantum spectra
Didactic derivation of Gutzwiller's trace formula from the path integral, with overview of its use in explaining random matrix theory statistics for quantum energy levels.
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Quantum graph models of quantum chaos: an introduction and some recent applications
Quantum graphs are presented as a paradigmatic model for quantum chaos, with the paper providing a didactical overview of foundational results and some recent developments.
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Quantum chaotic systems: a random-matrix approach
Review of random matrix theory application to quantum chaos, covering symmetry classes, eigenvalue statistics, unfolding, and correlation functions.