The inverse spectral problem for quantum semitoric systems
Résumé
We prove that semitoric systems are completely spectrally determined : from the joint spectrum of a quantum semitoric system, in the semiclassical limit, one can recover all symplectic invariants of the underlying classical semitoric system. Moreover, by using specific algorithms, we obtain a constructive way of doing so.
Mots clés
Semitoric integrable systems
Inverse spectral theory
Quantum mechanics
Semiclassical analysis
Pseudodifferential operators
Berezin-Toeplitz operators
Symplectic invariants
Focus-focus singularity
Joint spectrum
Asymptotic lattice
Good labelling
Quantum numbers
Lattice structure detection
Singular Lagrangian fibration
Semitoric integrable systems
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