Almost all eigenfunctions of a rational polygon are uniformly distributed

DOI10.4171/JST/23zbMath1242.37027arXiv1111.3583OpenAlexW2964068828MaRDI QIDQ414728

Jens Marklof, Ze'ev Rudnick

Publication date: 11 May 2012

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

Full work available at URL: https://arxiv.org/abs/1111.3583

zbMATH Keywords

quantum ergodicitybilliards in rational polygonspseudo-integrable systems

Mathematics Subject Classification ID

Quantum chaos (81Q50) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)

Related Items

Superscarred quasimodes on flat surfaces with conical singularities, Equidistribution of toral eigenfunctions along hypersurfaces, Quantum chaos for point scatterers on flat tori, Quadratic forms and semiclassical eigenfunction hypothesis for flat tori, Quantitative equidistribution of eigenfunctions for toral Schrödinger operators, Applications of small-scale quantum ergodicity in nodal sets, Concentration and non-concentration of eigenfunctions of second-order elliptic operators in layered media, \(L^{p}\) norms, nodal sets, and quantum ergodicity, Quantum ergodicity for a class of mixed systems, Quantum ergodicity and \(L^{p}\) norms of restrictions of eigenfunctions, Small scale equidistribution of eigenfunctions on the torus, Statistics of wave functions for a point scatterer on the torus, Eigenfunctions of Laplacians in some two-dimensional domains, Differences between Robin and Neumann eigenvalues, Polyhedral billiards, eigenfunction concentration and almost periodic control, Localization and delocalization of eigenmodes of harmonic oscillators, Around quantum ergodicity, An algorithm for identifying eigenvectors exhibiting strong spatial localization

Cites Work

• Statistics of wave functions for a point scatterer on the torus
• Ergodic billiards that are not quantum unique ergodic (with an appendix by Andrew Hassell and Luc Hillairet)
• Pseudointegrable systems in classical and quantum mechanics
• Ergodicity of billiard flows and quadratic differentials
• Polygonal billiards: correspondence between classical trajectories and quantum eigenstates
• Quantum limits on flat tori
• Ergodicity of eigenfunctions for ergodic billiards
• Quantum ergodicity of \(C^*\) dynamical systems
• Multiplicities of periodic orbit lengths for non-arithmetic models
• Eigenfunction Concentration for Polygonal Billiards