Schrödinger spectra and the effective Hamiltonian of weak KAM theory on the flat torus

DOI10.1063/1.4960741zbMath1344.81089OpenAlexW2510375805MaRDI QIDQ2820873

Lorenzo Zanelli

Publication date: 12 September 2016

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

Full work available at URL: http://hdl.handle.net/11577/3281292

zbMATH Keywords

Bohr-Sommerfeld quantization

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Hamilton-Jacobi equations in mechanics (70H20)

Related Items (6)

The geometry of the semiclassical wave front set for Schrödinger eigenfunctions on the torus ⋮ Periodic coherent states decomposition and quantum dynamics on the flat torus ⋮ A weak KAM approach to the periodic stationary Hartree equation ⋮ An exact version of the Egorov theorem for Schrödinger operators in \(L^2(\mathbb {T})\) ⋮ Dirac equation on the torus and rationally extended trigonometric potentials within supersymmetric QM ⋮ Schrödinger dynamics and optimal transport of measures

Cites Work

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• Some new PDE methods for weak KAM theory
• Towards a quantum analog of weak KAM theory
• Invariant tori, effective stability, and quasimodes with exponentially small error terms. I: Birkoff normal forms
• Quantum transport on KAM tori
• Non-Concentration of Quasimodes for Integrable Systems
• On Viscosity Solutions of Certain Hamilton–Jacobi Equations: Regularity Results and Generalized Sard's Theorems
• Effective Hamiltonians and averaging for Hamiltonian dynamics. I
• Quantum monodromy and Bohr-Sommerfeld rules

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