Semiclassical inverse spectral theory for singularities of focus-focus type

DOI10.1007/s00220-014-1998-9zbMath1345.81044arXiv1302.2260OpenAlexW3105600744MaRDI QIDQ2249766

Álvaro Pelayo, San Vũ Ngoc

Publication date: 3 July 2014

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

Full work available at URL: https://arxiv.org/abs/1302.2260

zbMATH Keywords

singularitiesfocus-focussemiclassical spectral inverse theory

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Hamilton's equations (70H05) Inverse problems for PDEs (35R30) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Pseudodifferential operators (47G30)

Related Items

Spectral asymptotics of semiclassical unitary operators, Symplectic and inverse spectral geometry of integrable systems: a glimpse and open problems, Symplectic invariants of semitoric systems and the inverse problem for quantum systems, Open problems, questions and challenges in finite- dimensional integrable systems, Asymptotic lattices, good labellings, and the rotation number for quantum integrable systems, Inverse spectral theory for semiclassical Jaynes-Cummings systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Smooth normal forms for integrable Hamiltonian systems near a focus-focus singularity
• First steps in symplectic and spectral theory of integrable systems
• Constructing integrable systems of semitoric type
• Spektrale Starrheit gewisser Drehflächen
• Homogeneous quantization and multiplicities of group representations
• Spectre conjoint d'opérateurs pseudo-différentiels qui commutent. II. Le cas intégrable
• Spectre conjoint d'opérateurs pseudo-différentiels qui commutent. I: Le cas non intégrable
• Quantum monodromy in integrable systems
• A note on focus-focus singularities
• The inverse spectral problem for surfaces of revolution
• On semi-global invariants for focus-focus singularities
• Semi-global symplectic invariants of the spherical pendulum
• Monodromy, diabolic points, and angular momentum coupling
• A semi-classical inverse problem I: Taylor expansions
• Symplectic inverse spectral theory for pseudodifferential operators
• Semiclassical quantization and spectral limits of ħ-pseudodifferential and Berezin-Toeplitz operators
• The quantum mechanical spherical pendulum
• On global action-angle coordinates
• Quasimodes and Bohr-Sommerfeld Conditions for the Toeplitz Operators
• Semiclassical eigenvalues and shape problems on surfaces of revolution
• Quantum states in a champagne bottle
• Inverse problems in spectral geometry
• Isospectrality for quantum toric integrable systems