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arXiv · 2403.05267

Integrable systems in magnetic fields: the generalized parabolic cylindrical case

O. Kubů·A. Marchesiello·L. Šnobl
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Abstract

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.

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O. Kubů, A. Marchesiello, L. Šnobl. 2024-03-08. Integrable systems in magnetic fields: the generalized parabolic cylindrical case. https://doi.org/10.1088/1751-8121%2Fad4936

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