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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.11440 |
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| _version_ | 1866910651319844864 |
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| author | Bourebai, Abdelkader Ghomari, Kaoutar Ngoc, San Vu |
| author_facet | Bourebai, Abdelkader Ghomari, Kaoutar Ngoc, San Vu |
| contents | The concept of near resonances for harmonic approximations of semiclassical Schrödinger operators is introduced and explored. Combined with a natural extension of the Birkhoff-Gustavson normal form, we obtain formulas for approaching the discrete spectrum of such operators which are both accurate and easy to implement. We apply the theory to the physically important case of the near Fermi 1:2 resonance, for which we propose explicit expressions and numerical computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semiclassical Birkhoff-Gustavson normal forms and spectral asymptotics for nearly resonant Schrödinger operators Bourebai, Abdelkader Ghomari, Kaoutar Ngoc, San Vu Spectral Theory Mathematical Physics The concept of near resonances for harmonic approximations of semiclassical Schrödinger operators is introduced and explored. Combined with a natural extension of the Birkhoff-Gustavson normal form, we obtain formulas for approaching the discrete spectrum of such operators which are both accurate and easy to implement. We apply the theory to the physically important case of the near Fermi 1:2 resonance, for which we propose explicit expressions and numerical computations. |
| title | Semiclassical Birkhoff-Gustavson normal forms and spectral asymptotics for nearly resonant Schrödinger operators |
| topic | Spectral Theory Mathematical Physics |
| url | https://arxiv.org/abs/2410.11440 |