Matrix oscillator and Calogero-type models
S. Meljanac, A. Samsarov
TL;DR
This paper introduces a matrix oscillator model with deformed commutation relations, establishing a new matrix realization of the Calogero model for identical particles without exchange operators, and discusses critical points of singular behavior.
Contribution
It presents a novel matrix oscillator framework linked to the Calogero model, avoiding exchange operators and exploring singularity points.
Findings
New matrix realization of the Calogero model for identical particles
Identification of critical points with singular behavior
Connection between matrix oscillator and multispecies Calogero model
Abstract
We study a single matrix oscillator with the quadratic Hamiltonian and deformed commutation relations. It is equivalent to the multispecies Calogero model in one dimension, with inverse-square two-body and three-body interactions. Specially, we have constructed a new matrix realization of the Calogero model for identical particles, without using exchange operators. The critical points at which singular behaviour occurs are briefly discussed.
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