Growth of Sobolev Norms in 1-d Quantum Harmonic Oscillator with Polynomial Time Quasi-periodic Perturbation

Jiawen Luo, Zhenguo Liang, Zhiyan Zhao

We consider the one-dimensional quantum harmonic oscillator perturbed by a linear operator which is a polynomial of degree $2$ in $(x,-\mathrm{i}{\partial }_x)$, with coefficients quasi-…