Integrable systems in magnetic fields: the generalized parabolic cylindrical case

Fuente: arXiv
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Autori principali: Kubů, O., Marchesiello, A., Šnobl, L.
Natura: Preprint
Pubblicazione: 2024
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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