The paper reviews spectral properties of operators for open quantum evolution and recent theoretical and experimental work on distinguishing chaotic from integrable dissipative quantum systems.
St ¨ockmann,Quantum Chaos: An Introduction, Cambridge University Press, Cambridge (1999), 10.1017/CBO9780511524622
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Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
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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What We Talk About When We Talk About Dissipative Quantum Chaos
The paper reviews spectral properties of operators for open quantum evolution and recent theoretical and experimental work on distinguishing chaotic from integrable dissipative quantum systems.
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Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
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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.