A duality relation extracts classical periodic orbits from the quantum spectrum of many-body systems like the kicked spin chain, with spectral statistics analyzed for coupled cat maps in the large semiclassical and particle-number limit.
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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.
The chapter reviews standard Hamiltonian chaos concepts including surfaces of section, stability analysis, symbolic dynamics, geometry of chaos, perturbation response, and complexification, with emphasis on intuitive illustrations for quantum chaos applications.
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The role of classical periodic orbits in quantum many-body systems
A duality relation extracts classical periodic orbits from the quantum spectrum of many-body systems like the kicked spin chain, with spectral statistics analyzed for coupled cat maps in the large semiclassical and particle-number limit.
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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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Hamiltonian Chaos
The chapter reviews standard Hamiltonian chaos concepts including surfaces of section, stability analysis, symbolic dynamics, geometry of chaos, perturbation response, and complexification, with emphasis on intuitive illustrations for quantum chaos applications.