It is proved that, under very restrictive conditins on the perturbation, the quantum Birkhoff normal form converges uniformly with respect to the Planck constant under the conditions of the classical Cherry theorem, namely dimension two and non real frequencies. This yields an exact quantization formula for the eigenvalues of the corresponding Schroedinger operator.

C.Villegas-Blas, S.Graffi (2008). A uniform quantum version of the Cherry theorem. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 278, 101-116 [10.1007/s00220-007-0380-6].

A uniform quantum version of the Cherry theorem

GRAFFI, SANDRO
2008

Abstract

It is proved that, under very restrictive conditins on the perturbation, the quantum Birkhoff normal form converges uniformly with respect to the Planck constant under the conditions of the classical Cherry theorem, namely dimension two and non real frequencies. This yields an exact quantization formula for the eigenvalues of the corresponding Schroedinger operator.
2008
C.Villegas-Blas, S.Graffi (2008). A uniform quantum version of the Cherry theorem. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 278, 101-116 [10.1007/s00220-007-0380-6].
C.Villegas-Blas; S.Graffi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/53960
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