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.File in questo prodotto:
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