On the rate of quantum ergodicity. I: Upper bounds

DOI10.1007/BF02099790zbMath0788.58043MaRDI QIDQ1317395

Steven Zelditch

Publication date: 31 May 1994

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Schrödinger operatorsspectral propertiesquantum ergodicityergodic geodesic flow

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (17)

Quantum variance for dihedral Maass forms ⋮ Quantum ergodicity for quantum graphs without back-scattering ⋮ Quantum variance and ergodicity for the baker's map ⋮ Equidistribution of toral eigenfunctions along hypersurfaces ⋮ Eigenfunction statistics on quantum graphs ⋮ Small‐scale equidistribution of Hecke eigenforms at infinity ⋮ \(L^{p}\) norms, nodal sets, and quantum ergodicity ⋮ On the rate of quantum ergodicity on hyperbolic surfaces and for billiards ⋮ Eigenstate thermalization hypothesis for Wigner matrices ⋮ Small scale equidistribution of eigenfunctions on the torus ⋮ Quantum variance for Hecke eigenforms☆ ⋮ Local average in hyperbolic lattice point counting, with an appendix by Niko Laaksonen ⋮ Quantum variance of Maass-Hecke cusp forms ⋮ On the spectral theory and dynamics of asymptotically hyperbolic manifolds ⋮ Quantitative quantum ergodicity and the nodal domains of Hecke-Maass cusp forms ⋮ Semiclassical limits for the hyperbolic plane ⋮ Rényi and Tsallis entropies related to eigenfunctions of quantum graphs

Cites Work

• Unnamed Item
• Ergodicity and eigenfunctions of the Laplacian
• Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• Mean Lindelöf hypothesis and equidistribution of cusp forms and Eisenstein series
• The central limit theorem for geodesic flows on \(n\)-dimensional manifolds of negative curvature
• A Dirichlet Series of Eigenvalue Type with Applications to Asymptotic Estimates
• The Riemann Hypothesis for Selberg's Zeta-Function and the Asymptotic Behavior of Eigenvalues of the Laplace Operator
• Improved two–term asymptotics for the eigenvalue distribution function of an elliptic operator on a compact manifold

This page was built for publication: On the rate of quantum ergodicity. I: Upper bounds