Quantum ergodicity for a class of mixed systems

DOI10.4171/JST/62zbMath1290.81037arXiv1209.2968MaRDI QIDQ2450828

Jeffrey Galkowski

Publication date: 21 May 2014

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.2968

zbMATH Keywords

quantum ergodicitysemiclassicalmixed dynamics

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items

Percival’s conjecture for the Bunimovich mushroom billiard, Macroscopic limits of chaotic eigenfunctions, Variations on quantum ergodic theorems, II, Around quantum ergodicity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Almost all eigenfunctions of a rational polygon are uniformly distributed
• Ergodicité et limite semi-classique. (Ergodicity and semi-classical limit)
• Ergodic billiards that are not quantum unique ergodic (with an appendix by Andrew Hassell and Luc Hillairet)
• Quantum leaks
• Ergodicity and eigenfunctions of the Laplacian
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• Ergodic properties of eigenfunctions for the Dirichlet problem
• Ergodicity of eigenfunctions for ergodic billiards
• Dispersion and controllability for the Schrödinger equation on negatively curved manifolds
• Remarks on quantum ergodicity
• Localization of Laplacian Eigenfunctions in Circular, Spherical, and Elliptical Domains
• The asymptotic solution of linear differential equations of the second order for large values of a parameter
• Quantum mushroom billiards
• Note on quantum unique ergodicity
• Weyl's law and quantum ergodicity for maps with divided phase space (with an appendix Converse quantum ergodicity)
• Quantum ergodicity for restrictions to hypersurfaces
• Quantum Monodromy and nonconcentration near a closed semi-hyperbolic orbit
• Mushrooms and other billiards with divided phase space