Superintegrability of separable systems with magnetic field: the cylindrical case

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F21%3A00352346" target="_blank" >RIV/68407700:21240/21:00352346 - isvavai.cz</a>

Alternative codes found

RIV/68407700:21340/21:00352346

Result on the web

<a href="https://doi.org/10.1088/1751-8121/ac2476" target="_blank" >https://doi.org/10.1088/1751-8121/ac2476</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8121/ac2476" target="_blank" >10.1088/1751-8121/ac2476</a>

Result language

angličtina

Original language name

Superintegrability of separable systems with magnetic field: the cylindrical case

Original language description

We present a general method simplifying the search for additional integrals of motion of three dimensional systems with magnetic fields. The method is suitable for systems possessing at least one conserved canonical momentum in a suitable coordinates system. It reduces the problem either to consideration of lower dimensional systems or of particular constrained forms of the hypothetical integral. In particular, it is applicable to all separable systems in the Euclidean space since they are known to possess at least one cyclic coordinates when magnetic field is present. Next, we focus on systems which separate in the cylindrical coordinates. Using our method, we are able to classify all superintegrable systems of this kind under the assumption that all considered integrals are at most second order in the momenta. In addition to already known systems, several new minimally superintegrable systems are found and we show that no quadratically maximally superintegrable ones can exist. We also construct some examples of systems with higher order integrals.

Czech name

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Czech description

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Type

J_imp - 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

2021

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Physics A: Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

1751-8121

Volume of the periodical

54

Issue of the periodical within the volume

42

Country of publishing house

GB - UNITED KINGDOM

Number of pages

38

Pages from-to

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UT code for WoS article

000701256200001

EID of the result in the Scopus database

2-s2.0-85116527464