We study the asymptotic behavior of the spectrum of a quantum system which is a perturbation of a spherically symmetric anharmonic oscillator in dimension 2. We prove that a large part of its eigenvalues can be obtained by Bohr-Sommerfeld quantization rule applied to the normal form Hamiltonian and also admits an asymptotic expansion at infinity. The proof is based on the generalization to the present context of the normal form approach developed in Bambusi et al. (Commun Part Differ Equ 45:1-18, 2020) (see also Parnovski and Sobolev in Invent Math 181(3):467-540, 2010) for the particular case of T-d.

On the Stable Eigenvalues of Perturbed Anharmonic Oscillators in Dimension Two / D. Bambusi, B. Langella, M. Rouveyrol. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 390:1(2022 Feb), pp. 309-348. [10.1007/s00220-021-04301-w]

On the Stable Eigenvalues of Perturbed Anharmonic Oscillators in Dimension Two

D. Bambusi
Primo
;
2022

Abstract

We study the asymptotic behavior of the spectrum of a quantum system which is a perturbation of a spherically symmetric anharmonic oscillator in dimension 2. We prove that a large part of its eigenvalues can be obtained by Bohr-Sommerfeld quantization rule applied to the normal form Hamiltonian and also admits an asymptotic expansion at infinity. The proof is based on the generalization to the present context of the normal form approach developed in Bambusi et al. (Commun Part Differ Equ 45:1-18, 2020) (see also Parnovski and Sobolev in Invent Math 181(3):467-540, 2010) for the particular case of T-d.
Settore MAT/07 - Fisica Matematica
Settore MAT/05 - Analisi Matematica
feb-2022
12-gen-2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/970461
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