Ergodic billiards that are not quantum unique ergodic (with an appendix by Andrew Hassell and Luc Hillairet)

DOI10.4007/annals.2010.171.605zbMath1196.58014arXiv0807.0666OpenAlexW1978683706MaRDI QIDQ974052

Andrew Hassell

Publication date: 27 May 2010

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.0666

zbMATH Keywords

eigenfunctionsBunimovich stadiumpartially rectangular domains

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)

Related Items (31)

Semiclassical scarring on tori in KAM Hamiltonian systems ⋮ High-girth near-Ramanujan graphs with localized eigenvectors ⋮ Recent progress on the quantum unique ergodicity conjecture ⋮ Superscarred quasimodes on flat surfaces with conical singularities ⋮ Note on converse quantum ergodicity ⋮ Superscars in the Šeba billiard ⋮ Percival’s conjecture for the Bunimovich mushroom billiard ⋮ Entropy of semiclassical measures in dimension 2 ⋮ Superscars for arithmetic point scatters II ⋮ Generic KAM Hamiltonians are not quantum ergodic ⋮ Entropic bounds on semiclassical measures for quantized one-dimensional maps ⋮ Almost all eigenfunctions of a rational polygon are uniformly distributed ⋮ Entropy of semiclassical measures for nonpositively curved surfaces ⋮ Quantum unique ergodicity for Cayley graphs of quasirandom groups ⋮ Macroscopic limits of chaotic eigenfunctions ⋮ Averaged pointwise bounds for deformations of Schrödinger eigenfunctions ⋮ Maximal scarring for eigenfunctions of quantum graphs ⋮ Quantum ergodicity for a class of mixed systems ⋮ Generic scarring for minimal hypersurfaces along stable hypersurfaces ⋮ Superscars for arithmetic toral point scatterers ⋮ Small scale equidistribution of random eigenbases ⋮ Small scale equidistribution of eigenfunctions on the torus ⋮ HOMOTOPIES OF EIGENFUNCTIONS AND THE SPECTRUM OF THE LAPLACIAN ON THE SIERPINSKI CARPET ⋮ Quantum ergodicity and symmetry reduction ⋮ Short geodesic loops and \(L^p\) norms of eigenfunctions on large genus random surfaces ⋮ High-Frequency Dynamics for the Schrödinger Equation, with Applications to Dispersion and Observability ⋮ Multifractal eigenfunctions for a singular quantum billiard ⋮ Localized eigenfunctions in Šeba billiards ⋮ A Non-Concentration Estimate for Partially Rectangular Billiards ⋮ Localization and delocalization of eigenmodes of harmonic oscillators ⋮ Around quantum ergodicity

Cites Work

• Unnamed Item
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• Mass equidistribution for Hecke eigenforms
• Ergodicity and eigenfunctions of the Laplacian
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• On the ergodic properties of nowhere dispersing billiards
• Ergodic properties of eigenfunctions for the Dirichlet problem
• 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
• Perturbation theory for linear operators.
• Quantum ergodicity of boundary values of eigenfunctions
• Ergodicity of eigenfunctions for ergodic billiards
• Entropy and the localization of eigenfunctions
• On quantum unique ergodicity for locally symmetric spaces
• Invariant measures and arithmetic unique ergodicity. Appendix by E. Lindenstrauss and D. Rudolph
• Condition nécessaire et suffisante pour la contrôlabilité exacte des ondes
• Note on quantum unique ergodicity
• Quantum Ergodicity of Boundary Values of Eigenfunctions: A Control Theory Approach
• Quantum unique ergodicity
• Bouncing Ball Modes and Quantum Chaos

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