KAM for high-dimensional nonlinear quantum harmonic oscillator
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909270655631360 |
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| author | Liu, Jianjun Qi, Caihong Shi, Guanghua |
| author_facet | Liu, Jianjun Qi, Caihong Shi, Guanghua |
| contents | In this paper, we study high-dimensional nonlinear quantum harmonic oscillator equation. We show the equation admits many time quasi-periodic solutions by establishing an abstract infinite dimensional KAM theorem with multiple normal frequencies. The proof is based on the classical KAM scheme, and the key is a decaying structure of Hessian matrices of Hamiltonian functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | KAM for high-dimensional nonlinear quantum harmonic oscillator Liu, Jianjun Qi, Caihong Shi, Guanghua Analysis of PDEs Dynamical Systems In this paper, we study high-dimensional nonlinear quantum harmonic oscillator equation. We show the equation admits many time quasi-periodic solutions by establishing an abstract infinite dimensional KAM theorem with multiple normal frequencies. The proof is based on the classical KAM scheme, and the key is a decaying structure of Hessian matrices of Hamiltonian functions. |
| title | KAM for high-dimensional nonlinear quantum harmonic oscillator |
| topic | Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2407.19312 |