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Séminaire Math-Phys : The quantum rotation number for 2D integrable systems

Mercredi 28 juin 16:45-17:45 - San Vũ Ngọc - Université de Rennes 1

Séminaire Math-Phys : The quantum rotation number for 2D integrable systems

Résumé : The rotation number (or "twist") of an integrable Hamiltonian system is a well-known dynamical quantity, whose irrationality can ensure the persistence of integrable dynamics under perturbation (KAM theory). Motivated by recent results on spectral asymptotics of some nonselfadjoint operators by Hitrik-Sjöstrand, we introduce a purely spectral number, the quantum rotation number, associated to a pair of commuting operators. Using this we prove that one can "hear" the classical rotation number, ie. one can detect it directly from the spectrum, in the semiclassical limit. We investigate the case of circular symmetry (semitoric systems), including numerics. Joint work with Monique Dauge and Mike Hall.

Lieu : Salle A318

Pour en savoir plus sur cet événement, consultez l'article Séminaires Math-Physique