Spectral asymptotics via the semiclassical Birkhoff normal form

DOI10.1215/00127094-2008-026zbMath1154.58015arXivmath/0605096OpenAlexW2118028127MaRDI QIDQ935195

Laurent Charles, San Vũ Ngoc

Publication date: 5 August 2008

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

Full work available at URL: https://arxiv.org/abs/math/0605096

zbMATH Keywords

spectral theorysemiclassical analysisglobal pseudo-differential operators

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Geometry and quantization, symplectic methods (81S10) Pseudodifferential and Fourier integral operators on manifolds (58J40) Momentum maps; symplectic reduction (53D20) Normal forms on manifolds (58K50)

Related Items (20)

Symplectic inverse spectral theory for pseudodifferential operators ⋮ Semiclassical analysis with vanishing magnetic fields ⋮ Koszul complexes, Birkhoff normal form and the magnetic Dirac operator ⋮ Non-commutative normal form, spectrum and inverse problem ⋮ Classical wave methods and modern gauge transforms: spectral asymptotics in the one dimensional case ⋮ The almost periodic gauge transform: an abstract scheme with applications to Dirac operators ⋮ Quantum Birkhoff-Gustavson normal form in some completely resonant cases ⋮ Airy functions and transition between semiclassical and harmonic oscillator approximations for one-dimensional bound states ⋮ Quantum mean-field asymptotics and multiscale analysis ⋮ Asymptotics of spectral clusters for a perturbation of the hydrogen atom ⋮ On calculating the coefficients in the quantum averaging procedure for the Hamiltonian of the resonance harmonic oscillator perturbed by a differential operator with polynomial coefficients ⋮ Normalization in Banach scale Lie algebras via mould calculus and applications ⋮ Singular Bohr-Sommerfeld Conditions for 1D Toeplitz Operators: Elliptic Case ⋮ Spectral monodromy of non-self-adjoint operators ⋮ Theta functions on the Kodaira–Thurston manifold ⋮ New approach to the procedure of quantum averaging for the Hamiltonian of a resonance harmonic oscillator with polynomial perturbation for the example of the spectral problem for the cylindrical Penning trap ⋮ Geometry and spectrum in 2D magnetic wells ⋮ A semiclassical Birkhoff normal form for symplectic magnetic wells ⋮ Construction of quasimodes for non-selfadjoint operators via propagation of Hagedorn wave-packets ⋮ Spectrum of semiclassical Schrödinger operators for two-frequency resonance

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles
• Autour de l'approximation semi-classique. (Around semiclassical approximation)
• Some spectral results for the Laplace operator with potential on the n- sphere
• Sur le spectre des opérateurs elliptiques à bicaracteristiques toutes périodiques
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• Moment maps and combinatorial invariants of Hamiltonian \(T^ n\)-spaces
• Clustering for the spectrum of \(h\)-pseudodifferential operators with periodic flow on an energy surface
• Berezin--Toeplitz operators, a semi-classical approach
• The inverse spectral problem for surfaces of revolution
• Wave-trace invariants
• Normal forms and quantization formulae
• Toeplitz operators and Hamiltonian torus actions
• New aspects in the theory of stability of Hamiltonian systems
• On a Hilbert space of analytic functions and an associated integral transform part I
• Multiple wells in the semi-classical limit I
• Birkhoff-Gustavson normal form in classical and quantum mechanics
• The Spectral Theory of Toeplitz Operators. (AM-99)
• Singular Bohr–Sommerfeld rules for 2D integrable systems
• On Riemann-Roch Formulas for Multiplicities

This page was built for publication: Spectral asymptotics via the semiclassical Birkhoff normal form