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- W2973025385 abstract "In this paper, the $d$-dimensional quantum harmonic oscillator with a pseudo-differential time quasi-periodic perturbation begin{equation}label{0} text{i}dot{psi}=(-Delta+V(x)+epsilon W(omega t,x,-text{i}nabla))psi, xinmathbb{R}^d end{equation} is considered, where $omegain(0,2pi)^n$, $V(x):=sum_{j=1}^d v_j^2x_j^2, v_jgeq v_0>0$, and $W(theta,x,xi)$ is a real polynomial in $(x,xi)$ of degree at most two, with coefficients belonging to $C^{ell}$ in $thetainmathbb{T}^n$ for the order $ell$ satisfying $ellgeq 2n-1+beta, 0<beta<1$. Using techniques developed by Bambusi-Gr'ebert-Maspero-Robert [emph{{Anal. PDE. 11(3):775-799, 2018}}] and Russmann [emph{pages 598--624. Lecture Notes in Phys., Vol. 38, 1975}], the paper shows that for any $|epsilon|leq epsilon_{star}(n,ell)$, there is a set $mathcal{D}_{epsilon}subset (0,2pi)^n$ with big Lebesgue measure, such that for any $omega inmathcal{D}_{epsilon}$, the system is reducible." @default.
- W2973025385 created "2019-09-19" @default.
- W2973025385 creator A5061580519 @default.
- W2973025385 date "2019-09-12" @default.
- W2973025385 modified "2023-09-27" @default.
- W2973025385 title "Reducibility of the quantum harmonic oscillator in $d$-dimensions with finitely differentiable perturbations" @default.
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- W2973025385 doi "https://doi.org/10.48550/arxiv.1909.05562" @default.
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