On rotationally invariant integrable and superintegrable classical systems in magnetic fields with non-subgroup type integrals

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F19%3A00331239" target="_blank" >RIV/68407700:21340/19:00331239 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1088/1751-8121/ab14c2" target="_blank" >https://doi.org/10.1088/1751-8121/ab14c2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8121/ab14c2" target="_blank" >10.1088/1751-8121/ab14c2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On rotationally invariant integrable and superintegrable classical systems in magnetic fields with non-subgroup type integrals

Popis výsledku v původním jazyce

The aim of the present article is to construct quadratically integrable three dimensional systems in non-vanishing magnetic fields which possess so-called non-subgroup type integrals. The presence of such integrals means that the system possesses a pair of integrals of motion in involution which are (at most) quadratic in momenta and whose leading order terms, that are necessarily elements of the enveloping algebra of the Euclidean algebra, are not quadratic Casimir operators of a chain of its subalgebras. By imposing in addition that one of the integrals has the leading order term L-z(2) we can consider three such commuting pairs: circular parabolic, oblate spheroidal and prolate spheroidal. We find all possible integrable systems possessing such structure of commuting integrals and describe their Hamiltonians and their integrals.

Název v anglickém jazyce

On rotationally invariant integrable and superintegrable classical systems in magnetic fields with non-subgroup type integrals

Popis výsledku anglicky

The aim of the present article is to construct quadratically integrable three dimensional systems in non-vanishing magnetic fields which possess so-called non-subgroup type integrals. The presence of such integrals means that the system possesses a pair of integrals of motion in involution which are (at most) quadratic in momenta and whose leading order terms, that are necessarily elements of the enveloping algebra of the Euclidean algebra, are not quadratic Casimir operators of a chain of its subalgebras. By imposing in addition that one of the integrals has the leading order term L-z(2) we can consider three such commuting pairs: circular parabolic, oblate spheroidal and prolate spheroidal. We find all possible integrable systems possessing such structure of commuting integrals and describe their Hamiltonians and their integrals.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA17-11805S" target="_blank" >GA17-11805S: Superintegrabilní systémy v magnetických polích ve třech prostorových rozměrech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Journal of Physics A: Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

1751-8121

Svazek periodika

52

Číslo periodika v rámci svazku

19

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

25

Strana od-do

—

Kód UT WoS článku

000464398800001

EID výsledku v databázi Scopus

2-s2.0-85065054813