Frozen planet orbits for the $n$-electron atom
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916988853420032 |
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| author | Baranzini, Stefano Canneori, Gian Marco Terracini, Susanna |
| author_facet | Baranzini, Stefano Canneori, Gian Marco Terracini, Susanna |
| contents | We seek periodic trajectories of a system of multiple mutually repelling electrons on a half-line, with an attractive nucleus sitting at the origin. We adopt a variational viewpoint and study critical points of the associated Lagrange-action functional, by means of a modified Lusternik-Schnirelmann theory for manifolds with boundary. Additionally, when the charges of the electrons tend to zero, we show that frozen planet orbits converge to segments of a brake orbit for a Kepler-type problem, establishing a strong analogy with the Schubart orbits of the gravitational $n$-body problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17848 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Frozen planet orbits for the $n$-electron atom Baranzini, Stefano Canneori, Gian Marco Terracini, Susanna Dynamical Systems 47J30, 34C25, 70F10, 34D15, 81V45 We seek periodic trajectories of a system of multiple mutually repelling electrons on a half-line, with an attractive nucleus sitting at the origin. We adopt a variational viewpoint and study critical points of the associated Lagrange-action functional, by means of a modified Lusternik-Schnirelmann theory for manifolds with boundary. Additionally, when the charges of the electrons tend to zero, we show that frozen planet orbits converge to segments of a brake orbit for a Kepler-type problem, establishing a strong analogy with the Schubart orbits of the gravitational $n$-body problem. |
| title | Frozen planet orbits for the $n$-electron atom |
| topic | Dynamical Systems 47J30, 34C25, 70F10, 34D15, 81V45 |
| url | https://arxiv.org/abs/2410.17848 |