Spectral asymptotics for sub-Riemannian Laplacians. I: Quantum ergodicity and quantum limits in the 3-dimensional contact case

DOI10.1215/00127094-2017-0037zbMath1388.35137arXiv1504.07112OpenAlexW2198721025WikidataQ115240682 ScholiaQ115240682MaRDI QIDQ1700517

Luc Hillairet, Yves Colin de Verdière, Emmanuel Trélat

Publication date: 6 March 2018

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.07112

zbMATH Keywords

quantum ergodicitycontact manifoldssub-Riemannian Laplacian

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Contact manifolds (general theory) (53D10) Geodesic flows in symplectic geometry and contact geometry (53D25)

Related Items

OBSERVABILITY OF BAOUENDI–GRUSHIN-TYPE EQUATIONS THROUGH RESOLVENT ESTIMATES, Semiclassical scarring on tori in KAM Hamiltonian systems, Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary, Null Controllability of the Parabolic Spherical Grushin Equation, Introducing sub-Riemannian and sub-Finsler billiards, Quantum ergodicity and quantum limits for sub-Riemannian Laplacians, Hyperbolicity, irrationality exponents and the eta invariant, Propagation of singularities for subelliptic wave equations, Sharp resolvent estimate for the damped-wave Baouendi-Grushin operator and applications, Quantum limits on product manifolds, Singular Weyl’s law with Ricci curvature bounded below, Spectral estimates and asymptotics for stratified Lie groups, Semi-classical analysis on H-type groups, Subelliptic wave equations are never observable, Quantum limits of sub-Laplacians via joint spectral calculus, Weyl's law for singular Riemannian manifolds, Spectral asymptotics for sub-Riemannian Laplacians. I: Quantum ergodicity and quantum limits in the 3-dimensional contact case, A proof of a trace formula by Richard Melrose, Towards semi-classical analysis for sub-elliptic operators, Kolmogorov-Fokker-Planck operators in dimension two: heat kernel and curvature, A Gutzwiller type trace formula for the magnetic Dirac operator, Microlocal Weyl formula on contact manifolds, Small-time asymptotics of hypoelliptic heat kernels near the diagonal, nilpotentization and related results, Quantum evolution and sub-Laplacian operators on groups of Heisenberg type, Defect measures on graded Lie groups, Estimates of eigenvalues for subelliptic operators on compact manifold

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantum ergodicity and quantum limits for sub-Riemannian Laplacians
• Ergodicité et limite semi-classique. (Ergodicity and semi-classical limit)
• Geometry and spectrum in 2D magnetic wells
• Ergodicity and eigenfunctions of the Laplacian
• The wave equation for a hypoelliptic operator with symplectic characteristics of codimension two
• The spectrum of the Laplacian on Riemannian Heisenberg manifolds
• Sub-Riemannian geometry
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• Sur le spectre des opérateurs elliptiques à bicaracteristiques toutes périodiques
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
• On the eigenvalues of a class of hypoelliptic operators
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• Ergodic properties of eigenfunctions for the Dirichlet problem
• Quantum limits on flat tori
• Neuer Beweis und Verallgemeinerung einiger Tauberian-Sätze
• Symbolic functional calculus and \(N\)-body resolvent estimates
• Spectral asymptotics for sub-Riemannian Laplacians. I: Quantum ergodicity and quantum limits in the 3-dimensional contact case
• Hearing the zero locus of a magnetic field
• Ergodicity of eigenfunctions for ergodic billiards
• Contact Anosov flows on hyperbolic 3-manifolds
• Trace heat kernel asymptotics in 3D contact sub-Riemannian geometry
• Hypoelliptic second order differential equations
• The spectral function of an elliptic operator
• Fourier integral operators. I
• Symplectic manifolds and their Lagrangian submanifolds
• Fourier integral operators. II
• The semiclassical theory of discontinuous systems and ray-splitting billiards
• Recent developments in mathematical Quantum Chaos
• The Spectral Theory of Toeplitz Operators. (AM-99)
• Hypoelliptic operators with double characteristics and related pseudo-differential operators
• Fonction spectrale et valeurs propres d'une classe d'operateurs non elliptiques
• An Introduction to Contact Topology
• Uniformisation et développement asymptotique de la solution du problème de Cauchy linéaire, à données holomorphes ; analogie avec la théorie des ondes asymptotiques et approchées (Problème de Cauchy I bis et VI.)
• Fourier integral operators