Note on quantum unique ergodicity

DOI10.1090/S0002-9939-03-07298-8zbMath1055.58016arXivmath-ph/0301035MaRDI QIDQ4461178

Steven Zelditch

Publication date: 29 March 2004

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0301035

zbMATH Keywords

Riemannian manifoldergodicityLaplacian

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) PDEs in connection with quantum mechanics (35Q40) Pseudodifferential and Fourier integral operators on manifolds (58J40)

Related Items (7)

Recent progress on the quantum unique ergodicity conjecture ⋮ Superscarred quasimodes on flat surfaces with conical singularities ⋮ Generic KAM Hamiltonians are not quantum ergodic ⋮ Quantum ergodicity for a class of mixed systems ⋮ Ergodic billiards that are not quantum unique ergodic (with an appendix by Andrew Hassell and Luc Hillairet) ⋮ Quantum leaks ⋮ Eigenfunctions for Partially Rectangular Billiards

Cites Work

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• Quasi-modes sur les variétés Riemanniennes
• The behaviour of eigenstates of arithmetic hyperbolic manifolds
• Scarred eigenstates for quantum cat maps of minimal periods
• On the maximal scarring for quantum cat map eigenstates
• Entropy of quantum limits
• Quantum transition amplitudes for ergodic and for completely integrable systems
• On the number of bouncing ball modes in billiards
• Quantum unique ergodicity
• Bouncing Ball Modes and Quantum Chaos
• The modulus of continuity for \(\Gamma_0(m)\backslash{\mathbb H}\) semi-classical limits

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