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Article Dans Une Revue Annales Scientifiques de l'École Normale Supérieure Année : 2013

Isospectrality for quantum toric integrable systems

Résumé

We settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of such a system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and Poisson commuting functions, up to symplectomorphisms. We also give a full description of the semiclassical spectral theory of quantum toric integrable systems. This type of problem belongs to the realm of classical questions in spectral theory going back to pioneer works of Colin de Verdiere, Guillemin, Sternberg and others in the 1970s and 1980s.

Dates et versions

hal-00707769 , version 1 (13-06-2012)

Identifiants

Citer

Laurent Charles, Alvaro Pelayo, San Vu Ngoc. Isospectrality for quantum toric integrable systems. Annales Scientifiques de l'École Normale Supérieure, 2013, 46 (5), pp.815-849. ⟨10.24033/asens.2202⟩. ⟨hal-00707769⟩
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