Integrable systems in magnetic fields: the generalized parabolic cylindrical case
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917696402096128 |
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| author | Kubů, O. Marchesiello, A. Šnobl, L. |
| author_facet | Kubů, O. Marchesiello, A. Šnobl, L. |
| contents | This article is a contribution to the classification of quadratically integrable systems with vector potentials whose integrals are of the nonstandard, nonseparable type. We focus on generalized parabolic cylindrical case, related to non-subgroup-type coordinates. We find 3 new systems, two with magnetic fields polynomial in Cartesian coordinates and one with unbounded exponential terms. The limit in the parameters of the integrals yields a new parabolic cylindrical system; the limit of vanishing magnetic fields leads to the free motion. This confirms the conjecture that non-subgroup type integrals can be related to separable systems only in a trivial manner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05267 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integrable systems in magnetic fields: the generalized parabolic cylindrical case Kubů, O. Marchesiello, A. Šnobl, L. Exactly Solvable and Integrable Systems Mathematical Physics This article is a contribution to the classification of quadratically integrable systems with vector potentials whose integrals are of the nonstandard, nonseparable type. We focus on generalized parabolic cylindrical case, related to non-subgroup-type coordinates. We find 3 new systems, two with magnetic fields polynomial in Cartesian coordinates and one with unbounded exponential terms. The limit in the parameters of the integrals yields a new parabolic cylindrical system; the limit of vanishing magnetic fields leads to the free motion. This confirms the conjecture that non-subgroup type integrals can be related to separable systems only in a trivial manner. |
| title | Integrable systems in magnetic fields: the generalized parabolic cylindrical case |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2403.05267 |