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

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/68407700:21340/23:00366296

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Centrum pokročilých aplikovaných přírodních věd</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Annals of Physics

ISSN

0003-4916

e-ISSN

1096-035X

Svazek periodika

451

Číslo periodika v rámci svazku

169264

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

24

Strana od-do

—

Kód UT WoS článku

000953371300001

EID výsledku v databázi Scopus

2-s2.0-85149468299