Reducibility of the quantum harmonic oscillator in $d$-dimensions with finitely differentiable perturbations

Abstract

In this paper, the d-dimensional quantum harmonic oscillator with a pseudodifferential time quasi-periodic perturbation) is a real polynomial in (x, ξ) of degree at most two, with coefficients belonging to C ℓ in θ ∈ T n for the order ℓ satisfying ℓ ≥ 2n − 1 + β, 0 < β < 1.Using techniques developed by Bambusi-Grébert-Maspero-Robert [Anal.