Variations on quantum ergodic theorems

DOI10.1007/S11118-015-9489-YzbMath1432.58029OpenAlexW793200419MaRDI QIDQ907312

Michael E. Taylor

Publication date: 25 January 2016

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11118-015-9489-y

zbMATH Keywords

chaosspectrumeigenfunctionquantum ergodic theorem

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Quantum chaos (81Q50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)

Related Items (4)

Applications of small-scale quantum ergodicity in nodal sets ⋮ Variations on quantum ergodic theorems, II ⋮ Quantum ergodicity and \(L^{p}\) norms of restrictions of eigenfunctions ⋮ Microlocal Weyl formula on contact manifolds

Cites Work

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• Ergodicité et limite semi-classique. (Ergodicity and semi-classical limit)
• Ergodicity and eigenfunctions of the Laplacian
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• Chaos in classical and quantum mechanics
• Semiclassical asymptotics, gauge fields, and quantum chaos
• Stable and Random Motions in Dynamical Systems
• Quantum mushroom billiards
• Quantum unique ergodicity
• Relative volume of Kolmogorov–Arnold–Moser tori and uniform distribution, stickiness and nonstickiness in Hamiltonian systems
• Mushrooms and other billiards with divided phase space

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