Calogero-like Model without Rearrangement Symmetry

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F24%3A00582660" target="_blank" >RIV/61389005:_____/24:00582660 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/62690094:18470/24:50021221

Výsledek na webu

<a href="https://doi.org/10.3390/sym16010027" target="_blank" >https://doi.org/10.3390/sym16010027</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/sym16010027" target="_blank" >10.3390/sym16010027</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Calogero-like Model without Rearrangement Symmetry

Popis výsledku v původním jazyce

Reinterpretation of mathematics behind the exactly solvable Calogero's A-particle quantum model is used to propose its generalization. Firstly, it is argued that the strongly singular nature of Calogero's particle-particle interactions makes the original permutation-invariant Hamiltonian tractable as a direct sum H - circle plus H-a of isospectral components, which are mutually independent. Secondly, after the elimination of the center-of-mass motion, the system is reconsidered as existing in the reduced Euclidean space RA-1 of relative coordinates and decaying into a union of subsets W-a called Weyl chambers. The mutual independence of the related reduced forms of operators H-a enables us to makes them nonisospectral. This breaks the symmetry and unfolds the spectral degeneracy of H. A new multiparametric generalization of the conventional A-body Calogero model is obtained. Its detailed description is provided up to A = 4.

Název v anglickém jazyce

Calogero-like Model without Rearrangement Symmetry

Popis výsledku anglicky

Reinterpretation of mathematics behind the exactly solvable Calogero's A-particle quantum model is used to propose its generalization. Firstly, it is argued that the strongly singular nature of Calogero's particle-particle interactions makes the original permutation-invariant Hamiltonian tractable as a direct sum H - circle plus H-a of isospectral components, which are mutually independent. Secondly, after the elimination of the center-of-mass motion, the system is reconsidered as existing in the reduced Euclidean space RA-1 of relative coordinates and decaying into a union of subsets W-a called Weyl chambers. The mutual independence of the related reduced forms of operators H-a enables us to makes them nonisospectral. This breaks the symmetry and unfolds the spectral degeneracy of H. A new multiparametric generalization of the conventional A-body Calogero model is obtained. Its detailed description is provided up to A = 4.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Symmetry-Basel

ISSN

2073-8994

e-ISSN

2073-8994

Svazek periodika

16

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

20

Strana od-do

27

Kód UT WoS článku

001152706100001

EID výsledku v databázi Scopus

2-s2.0-85183104913