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arXiv · 2108.08141

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

Jiawen Luo·Zhenguo Liang·Zhiyan Zhao
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Abstract

We consider the one-dimensional quantum harmonic oscillator perturbed by a linear operator which is a polynomial of degree $2$ in $(x,-{\rm i}\partial_x)$, with coefficients quasi-periodically depending on time. By establishing the reducibility results, we describe the growth of Sobolev norms. In particular, the $t^{2s}-$polynomial growth of ${\mathcal H}^s-$norm is observed in this model if the original time quasi-periodic equation is reduced to a constant Stark Hamiltonian.

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Jiawen Luo, Zhenguo Liang, Zhiyan Zhao. 2021-08-18. Growth of Sobolev Norms in 1-d Quantum Harmonic Oscillator with Polynomial Time Quasi-periodic Perturbation. https://doi.org/10.1007/s00220-022-04340-x

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