Symplectic invariants of semitoric systems and the inverse problem for quantum systems

DOI10.1016/j.indag.2020.04.005zbMath1469.37046arXiv2002.05306OpenAlexW3022503808MaRDI QIDQ2219494

Álvaro Pelayo

Publication date: 20 January 2021

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.05306

zbMATH Keywords

focus-focus singularitiessymplectic invariantssemitoric systems

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Exactly and quasi-solvable systems arising in quantum theory (81U15) Geometric quantization (53D50) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items

Symplectic and inverse spectral geometry of integrable systems: a glimpse and open problems ⋮ Vũ Ngọc's conjecture on focus-focus singular fibers with multiple pinched points ⋮ The height invariant of a four-parameter semitoric system with two focus-focus singularities ⋮ A family of semitoric systems with four focus-focus singularities and two double pinched tori

Cites Work

• Generating hyperbolic singularities in semitoric systems via Hopf bifurcations
• Smooth normal forms for integrable Hamiltonian systems near a focus-focus singularity
• Symplectic spectral geometry of semiclassical operators
• Diophantine tori and non-selfadjoint inverse spectral problems
• Symplectic and Poisson geometry on \( b\)-manifolds
• First steps in symplectic and spectral theory of integrable systems
• From compact semi-toric systems to Hamiltonian \(S^1\)-spaces
• The tropical momentum map: a classification of toric log symplectic manifolds
• Constructing integrable systems of semitoric type
• Berezin-Toeplitz quantization for compact Kähler manifolds. A review of results
• Hamiltonian dynamics and spectral theory for SPIN-oscillators
• Minimal models of compact symplectic semitoric manifolds
• Lectures on torus embeddings and applications. (Based on joint work with Katsuya Miyake.)
• Spektrale Starrheit gewisser Drehflächen
• Homogeneous quantization and multiplicities of group representations
• Semitoric integrable systems on symplectic 4-manifolds
• Connectivity properties of moment maps on based loop groups
• Toric symplectic ball packing
• Moment polytopes for symplectic manifolds with monodromy
• Symbolic calculus for Toeplitz operators with half-form
• Semi-classical properties of geometric quantization with metaplectic correction
• Non-compact symplectic toric manifolds
• Asymptotics of action variables near semi-toric singularities
• Normal forms for Hamiltonian systems with Poisson commuting integrals - elliptic case
• Toeplitz operators on symplectic manifolds
• Quantification géométrique.
• Almost toric symplectic four-manifolds
• Spectre conjoint d'opérateurs pseudo-différentiels qui commutent. II. Le cas intégrable
• On the variation in the cohomology of the symplectic form of the reduced phase space
• Convexity properties of the moment mapping
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Spectre conjoint d'opérateurs pseudo-différentiels qui commutent. I: Le cas non intégrable
• Semiclassical spectral estimates for Toeplitz operators
• On Poisson actions of compact Lie groups on symplectic manifolds
• Berezin--Toeplitz operators, a semi-classical approach
• Momentum maps and Hamiltonian reduction
• Actions symplectiques de groupes compacts. (Symplectic actions of compact groups)
• Global action-angle variables for non-commutative integrable systems
• Faithful semitoric systems
• On the density function on moduli spaces of toric 4-manifolds
• A family of compact semitoric systems with two focus-focus singularities
• Classifying toric and semitoric fans by lifting equations from \(\mathrm{SL}_2(\mathbb{Z})\)
• Integrable systems, symmetries, and quantization
• The inverse spectral problem for surfaces of revolution
• On semi-global invariants for focus-focus singularities
• Monodromy, diabolic points, and angular momentum coupling
• Moduli spaces of toric manifolds
• Semiclassical inverse spectral theory for singularities of focus-focus type
• Convexity properties of the moment mapping. III
• Correction to: ``Inverse spectral theory for semiclassical Jaynes-Cummings systems
• Fiber connectivity and bifurcation diagrams of almost toric integrable systems
• Moduli spaces of semitoric systems
• Taylor series and twisting-index invariants of coupled spin-oscillators
• Symplectic geometry and spectral properties of classical and quantum coupled angular momenta
• Symplectic torus actions with coisotropic principal orbits
• Toeplitz operators and Hamiltonian torus actions
• Spectral asymptotics of semiclassical unitary operators
• 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
• Spectral limits of semiclassical commuting self-adjoint operators
• Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems
• Symplectic theory of completely integrable Hamiltonian systems
• Introduction to Toric Varieties. (AM-131)
• Topology of spaces of equivariant symplectic embeddings
• Maximal Ball Packings of Symplectic-Toric Manifolds
• Symplectic actions of 2-tori on 4-manifolds
• Reduced phase space and toric variety coordinatizations of Delzant spaces
• The quantum mechanical spherical pendulum
• Hamiltoniens périodiques et images convexes de l'application moment
• On global action-angle coordinates
• Symplectic geometry
• The Spectral Theory of Toeplitz Operators. (AM-99)
• Convexity and Commuting Hamiltonians
• Periodic Hamiltonian flows on four-dimensional manifolds
• A convexity theorem for Poisson actions of compact Lie groups
• Quasimodes and Bohr-Sommerfeld Conditions for the Toeplitz Operators
• The affine invariant of proper semitoric integrable systems
• Open problems, questions and challenges in finite- dimensional integrable systems
• Symplectic G-capacities and integrable systems
• Semiclassical eigenvalues and shape problems on surfaces of revolution
• Quantum states in a champagne bottle
• Hamiltonian and symplectic symmetries: An introduction
• Symplectic classification of coupled angular momenta
• Isospectrality for quantum toric integrable systems
• Removing a Ray from a Noncompact Symplectic Manifold
• Poisson geometry of discrete series orbits, and momentum convexity for noncompact group actions
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