Canonical forms for perturbations of the harmonic oscillator

2013/07/27 by Guillemin, Victor, Uribe, Alejandro, Wang, Zuoqin
#35P20 #37J40 #81Q20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1307.7227

Abstract

We consider a class of perturbations of the 2D harmonic oscillator, and of some other dynamical systems, which we show are isomorphic to a function of a toric system (a Birkhoff canonical form). We show that for such systems there exists a quantum normal form as well, which is determined by spectral data.

Related

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• The semi-classical spectrum and the Birkhoff normal form
• Concentration of Quasimodes for Perturbed Harmonic Oscillators
• Diophantine tori and nonselfadjoint inverse spectral problems
• Quantum Birkhoff Normal Form in the σ-Bruno-Rüssmann non-resonant condition