2011/02/04 by Sandro Graffi, Graffi, Sandro, Thierry Paul +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.DS #math.MP
paper · pdf · doi:10.48550/arxiv.1102.0942
new revised version, with correction of some little mistakes
openalex publication_date 2011/02/04 · arxiv created 2011/12/23 · arxiv updated 2011/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the Schrödinger operator defined by the quantization of the linear flow of diophantine frequencies over the l-dimensional torus, perturbed by a holomorphic potential which depends on the actions only through their particular linear combination defining the Hamiltonian of the linear flow. We prove that the corresponding quantum normal form converges uniformly with respect to the Planck constant. This result simultaneously yields an exact quantization formula for the quantum spectrum, as well as a convergence criterion for the Birkhoff normal form, valid for a class of perturbations holomorphic away from the origin.