Quantum transition amplitudes for ergodic and for completely integrable systems

DOI10.1016/0022-1236(90)90021-CzbMath0721.58051OpenAlexW1978676081MaRDI QIDQ2640976

Steven Zelditch

Publication date: 1990

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(90)90021-c

zbMATH Keywords

eigenfunctionsgeodesic flowsLaplacianmixing flowcompletely integrable flows

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Geodesic flows in symplectic geometry and contact geometry (53D25) Ergodic theory (37A99) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (15)

Classicality criteria ⋮ Quantum ergodicity of \(C^*\) dynamical systems ⋮ On the rate of Quantum Ergodicity, II: Lower bounds ⋮ Quantum ergodicity and localization of plasmon resonances ⋮ Quantum limits of sub-Laplacians via joint spectral calculus ⋮ Semiclassical sum rules and generalized coherent states ⋮ Intertwining the geodesic flow and the Schrödinger group on hyperbolic surfaces ⋮ Unnamed Item ⋮ Index and dynamics of quantized contact transformations ⋮ On a semiclassical formula for non-diagonal matrix elements ⋮ Quantum ergodicity on the sphere ⋮ Note on quantum unique ergodicity ⋮ Unnamed Item ⋮ Riemannian manifolds with uniformly bounded eigenfunctions ⋮ Ergodic properties of the quantum geodesic flow on tori

Cites Work

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• The weyl calculus of pseudo-differential operators
• On the Space of Invariant Measures for Hyperbolic Flows
• Lectures on spectral theory of elliptic operators

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