New classes of quadratically integrable systems in magnetic fields: The generalized cylindrical and spherical cases

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00366296" target="_blank" >RIV/68407700:21240/23:00366296 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/23:00366296
Result on the web
<a href="https://doi.org/10.1016/j.aop.2023.169264" target="_blank" >https://doi.org/10.1016/j.aop.2023.169264</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aop.2023.169264" target="_blank" >10.1016/j.aop.2023.169264</a>

Result language
angličtina
Original language name
New classes of quadratically integrable systems in magnetic fields: The generalized cylindrical and spherical cases
Original language description
We study integrable and superintegrable systems with magnetic field possessing quadratic integrals of motion on the three-dimensional Euclidean space. In contrast with the case without vector potential, the corresponding integrals may no longer be connected to separation of variables in the Hamilton-Jacobi equation and can have more general leading order terms. We focus on two cases extending the physically relevant cylindrical -and spherical-type integrals. We find three new integrable sys-tems in the generalized cylindrical case but none in the spherical one. We conjecture that this is related to the presence, respec-tively absence, of maximal abelian Lie subalgebra of the three-dimensional Euclidean algebra generated by first order integrals in the limit of vanishing magnetic field. By investigating superin-tegrability, we find only one (minimally) superintegrable system among the integrable ones. It does not separate in any orthogonal coordinate system. This system provides a mathematical model of a helical undulator placed in an infinite solenoid. (c) 2023 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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