Calogero-like Model without Rearrangement Symmetry - INSPIRE

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Calogero-like Model without Rearrangement Symmetry

Miloslav Znojil

Dec 21, 2023

30 pages

Published in:

Symmetry 16 (2024) 1, 27,
Symmetry 16 (2024) 0027

Published: Dec 24, 2023

e-Print:

2312.13667 [nlin.SI]

DOI:

10.3390/sym16010027

View in:

ADS Abstract Service

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Abstract: (MDPI)

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 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 of relative coordinates and decaying into a union of subsets called Weyl chambers. The mutual independence of the related reduced forms of operators 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 .

Note:

30 pages, 9 figures

Calogero’s AN model
asymmetric two-particle barriers
exact solvability requirement
coloring of the Weyl chambers

References(54)

Figures(9)

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