Birkhoff normal form in low regularity for the nonlinear quantum harmonic oscillator
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866911817168584704 |
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| author | Khalil, Charbella Abou |
| author_facet | Khalil, Charbella Abou |
| contents | Given small initial solutions of the nonlinear quantum harmonic oscillator on $\mathbb{R}$, we are interested in their long time behavior in the energy space which is an adapted Sobolev space. We perturbate the linear part by $V$ taken as multiplicative potentials, in a way that the linear frequencies satisfy a non-resonance condition. More precisely, we prove that for almost all potentials $V$, the low modes of the solution are almost preserved for very long times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_13076 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Birkhoff normal form in low regularity for the nonlinear quantum harmonic oscillator Khalil, Charbella Abou Analysis of PDEs Mathematical Physics Given small initial solutions of the nonlinear quantum harmonic oscillator on $\mathbb{R}$, we are interested in their long time behavior in the energy space which is an adapted Sobolev space. We perturbate the linear part by $V$ taken as multiplicative potentials, in a way that the linear frequencies satisfy a non-resonance condition. More precisely, we prove that for almost all potentials $V$, the low modes of the solution are almost preserved for very long times. |
| title | Birkhoff normal form in low regularity for the nonlinear quantum harmonic oscillator |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2211.13076 |