On the reducibility of the 1d quantum harmonic oscillator with a quasi-periodic bounded potential
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915473196580864 |
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| author | Haus, Emanuele Wang, Zhiqiang |
| author_facet | Haus, Emanuele Wang, Zhiqiang |
| contents | Using the decay along the diagonal of the matrix representing the perturbation with respect to the Hermite basis, we prove a reducibility result in $L^2(\mathbb{R})$ for the one-dimensional quantum harmonic oscillator perturbed by time quasi-periodic potential, via a KAM iteration. The potential is only bounded (no decay at infinity is required) and its derivative with respect to the spatial variable $x$ is allowed to grow at most like $|x|^δ$ when $x$ goes to infinity, where the power $δ<1$ is arbitrary. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_01484 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the reducibility of the 1d quantum harmonic oscillator with a quasi-periodic bounded potential Haus, Emanuele Wang, Zhiqiang Dynamical Systems Functional Analysis 37K55 Using the decay along the diagonal of the matrix representing the perturbation with respect to the Hermite basis, we prove a reducibility result in $L^2(\mathbb{R})$ for the one-dimensional quantum harmonic oscillator perturbed by time quasi-periodic potential, via a KAM iteration. The potential is only bounded (no decay at infinity is required) and its derivative with respect to the spatial variable $x$ is allowed to grow at most like $|x|^δ$ when $x$ goes to infinity, where the power $δ<1$ is arbitrary. |
| title | On the reducibility of the 1d quantum harmonic oscillator with a quasi-periodic bounded potential |
| topic | Dynamical Systems Functional Analysis 37K55 |
| url | https://arxiv.org/abs/2509.01484 |