Cylindrical first-order superintegrability with complex magnetic fields

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00368472" target="_blank" >RIV/68407700:21340/23:00368472 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1063/5.0138095" target="_blank" >https://doi.org/10.1063/5.0138095</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/5.0138095" target="_blank" >10.1063/5.0138095</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Cylindrical first-order superintegrability with complex magnetic fields

Popis výsledku v původním jazyce

This article is a contribution to the study of superintegrable Hamiltonian systems with magnetic fields on the three-dimensional Euclidean space E-3 in quantum mechanics. In contrast to the growing interest in complex electromagnetic fields in the mathematical community following the experimental confirmation of its physical relevance [Peng et al., Phys. Rev. Lett. 114, 010601 (2015)], they were so far not addressed in the growing literature on superintegrability. Here, we venture into this field by searching for additional first-order integrals of motion to the integrable systems of cylindrical type. We find that already known systems can be extended into this realm by admitting complex coupling constants. In addition to them, we find one new system whose integrals of motion also feature complex constants. All these systems are multiseparable. Rigorous mathematical analysis of these systems is challenging due to the non-Hermitian setting and lost gauge invariance. We proceed formally and pose the resolution of these problems as an open challenge.

Název v anglickém jazyce

Cylindrical first-order superintegrability with complex magnetic fields

Popis výsledku anglicky

This article is a contribution to the study of superintegrable Hamiltonian systems with magnetic fields on the three-dimensional Euclidean space E-3 in quantum mechanics. In contrast to the growing interest in complex electromagnetic fields in the mathematical community following the experimental confirmation of its physical relevance [Peng et al., Phys. Rev. Lett. 114, 010601 (2015)], they were so far not addressed in the growing literature on superintegrability. Here, we venture into this field by searching for additional first-order integrals of motion to the integrable systems of cylindrical type. We find that already known systems can be extended into this realm by admitting complex coupling constants. In addition to them, we find one new system whose integrals of motion also feature complex constants. All these systems are multiseparable. Rigorous mathematical analysis of these systems is challenging due to the non-Hermitian setting and lost gauge invariance. We proceed formally and pose the resolution of these problems as an open challenge.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

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

Journal of Mathematical Physics

ISSN

0022-2488

e-ISSN

1089-7658

Svazek periodika

64

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

"062101-1"-"062101-12"

Kód UT WoS článku

001027447600006

EID výsledku v databázi Scopus

2-s2.0-85161044623