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arXiv · 2111.11678

Reducibility of Quantum Harmonic Oscillator on $\mathbb{R}^d$ Perturbed by a Quasi-periodic Potential with Logarithmic Decay

Zhenguo Liang·Zhiqiang Wang
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Abstract

We prove the reducibility of quantum harmonic oscillators in $\mathbb R^d$ perturbed by a quasi-periodic in time potential $V(x,\omega t)$ with $\mathit{logarithmic~decay}$. By a new estimate built for solving the homological equation we improve the reducibility result by Gr\'ebert-Paturel(Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques. $\mathbf{28}$, 2019).

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Zhenguo Liang, Zhiqiang Wang. 2021-11-23. Reducibility of Quantum Harmonic Oscillator on $\mathbb{R}^d$ Perturbed by a Quasi-periodic Potential with Logarithmic Decay. https://arxiv.org/abs/2111.11678

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