1-d Quantum Harmonic Oscillator with Time Quasi-periodic Quadratic Perturbation: Reducibility and Growth of Sobolev Norms

Zhenguo Liang, Zhiyan Zhao, Qi Zhou

For a family of 1-d quantum harmonic oscillator with a perturbation which is $C^2$ parametrized by $E\in \mathcal{I}\subset \mathbb{R}$ and quadratic on $x$ and $-\mathrm{i}{\partial }_x$ w…