Symplectic geometry and spectral properties of classical and quantum coupled angular momenta

DOI10.1007/s00332-018-9501-yzbMath1417.53085arXiv1607.05419OpenAlexW2963657557MaRDI QIDQ2423393

Álvaro Pelayo, Yohann Le Floch

Publication date: 21 June 2019

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.05419

zbMATH Keywords

symplectic geometryintegrable systemssemiclassical analysissemitoric systems

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) 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) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)

Related Items

Symplectic and inverse spectral geometry of integrable systems: a glimpse and open problems, Packing densities of Delzant and semitoric polygons, Constructions of b-semitoric systems, Vũ Ngọc's conjecture on focus-focus singular fibers with multiple pinched points, Hamiltonian and symplectic symmetries: An introduction, Symplectic invariants of semitoric systems and the inverse problem for quantum systems, Characterization of toric systems via transport costs, A family of compact semitoric systems with two focus-focus singularities, Minimal models of compact symplectic semitoric manifolds, The height invariant of a four-parameter semitoric system with two focus-focus singularities, Symplectic classification of coupled angular momenta, Existence of pseudoheavy fibers of moment maps, Asymptotic lattices, good labellings, and the rotation number for quantum integrable systems

Cites Work

• Unnamed Item
• Unnamed Item
• 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
• A Künneth formula for coherent algebraic sheaves
• Semitoric integrable systems on symplectic 4-manifolds
• Moment polytopes for symplectic manifolds with monodromy
• Symbolic calculus for Toeplitz operators with half-form
• Toeplitz operators on symplectic manifolds
• Quantification géométrique.
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem.
• Convexity properties of the moment mapping
• Dispersionless Toda and Toeplitz operators
• \(L^p\) norms of eigenfunctions in the completely integrable case
• Berezin--Toeplitz operators, a semi-classical approach
• A family of compact semitoric systems with two focus-focus singularities
• Integrable systems, symmetries, and quantization
• On semi-global invariants for focus-focus singularities
• Semi-global symplectic invariants of the spherical pendulum
• Monodromy, diabolic points, and angular momentum coupling
• Taylor series and twisting-index invariants of coupled spin-oscillators
• Singular Bohr-Sommerfeld conditions for 1D Toeplitz operators: hyperbolic case
• Classical and quantum integrability
• Symplectic theory of completely integrable Hamiltonian systems
• The Spectral Theory of Toeplitz Operators. (AM-99)
• Convexity and Commuting Hamiltonians
• The affine invariant of proper semitoric integrable systems
• Hamiltonian and symplectic symmetries: An introduction
• Singular Bohr-Sommerfeld Conditions for 1D Toeplitz Operators: Elliptic Case
• Quantization and unitary representations
• On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems