Superintegrability of separable systems with magnetic field: the cylindrical case

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/68407700:21340/21:00352346

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Superintegrability of separable systems with magnetic field: the cylindrical case

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Superintegrability of separable systems with magnetic field: the cylindrical case

Popis výsledku anglicky

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.

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

2021

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

54

Číslo periodika v rámci svazku

42

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

38

Strana od-do

—

Kód UT WoS článku

000701256200001

EID výsledku v databázi Scopus

2-s2.0-85116527464