Behavior of a constrained particle on superintegrability of the two-dimensional complex Cayley–Klein space and its thermodynamic properties

Najafizade, Amene; Panahi, H.

doi:10.1016/j.physa.2021.125935

Cited by 4 publications

(2 citation statements)

References 39 publications

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“…The relations involved for these κ-dependent functions can be found in [22][23][24][25]] (10) and definition of the κ-tangent is as T κ (x) = S κ (x)/C κ (x). The curved oscillator potential subjected to the governing spaces represented the following expression…”

Section: Curved Dunkl Oscillator Model and Geodesic Motionmentioning

confidence: 99%

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Superintegrability on the Dunkl oscillator model in three-Dimensional spaces of constant curvature

Dong,

Najafizade,

Panahi

et al. 2021

Preprint

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This paper has studied the three-dimensional Dunkl oscillator models in a generalization of superintegrable Euclidean Hamiltonian systems to curved ones. These models are defined based on curved Hamiltonians, which depend on a deformation parameter of underlying space and involve reflection operators. Their symmetries are obtained by the Jordan-Schwinger representations in the family of the Cayley-Klein orthogonal algebras using the creation and annihilation operators of the dynamical sl −1 (2) algebra of the one-dimensional Dunkl oscillator. The resulting algebra is a deformation of so κ 1 κ 2 (4) with reflections, which is known as the Jordan-Schwinger-Dunkl algebra jsd κ 1 κ 2 (4). Hence, this model is shown to be maximal superintegrable. On the other hand, the superintegrability of the three-dimensional Dunkl oscillator model is studied from the factorization approach viewpoint. The spectrum of this system is derived through the separation of variables in geodesic polar coordinates, and the resulting eigenfunctions are algebraically given in terms of Jacobi polynomials.

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Section: Curved Dunkl Oscillator Model and Geodesic Motionmentioning

confidence: 99%

“…such that κ 3 = 1 is considered here. Thus, the Jordan-Schwinger construction (24) of Lie generators so κ 1 κ 2 (4) is shown in making use of the creation and annihilation operators (19), as follows ( j = 2, 3)…”

Section: Curved Dunkl Oscillator Model and Geodesic Motionmentioning

confidence: 99%

Superintegrability on the Dunkl oscillator model in three-Dimensional spaces of constant curvature

Dong,

Najafizade,

Panahi

et al. 2021

Preprint

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Superintegrability on the Dunkl oscillator model in three-dimensional spaces of constant curvature

et al. 2022

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The anisotropic Dunkl oscillator problem on the two-dimensional curved spaces

Najafizade

Panahi

2022

Mod. Phys. Lett. A

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In this paper, we study the two-dimensional (2D) Euclidean anisotropic Dunkl oscillator model in an integrable generalization to curved ones of the 2D sphere [Formula: see text] and the hyperbolic plane [Formula: see text]. This generalized model depends on the deformation parameter [Formula: see text] of underlying space and involves reflection operators [Formula: see text] in such a way that all the results are simultaneously valid for [Formula: see text], [Formula: see text] and [Formula: see text]. It turns out that this system is superintegrable based on the special cases of parameter [Formula: see text], which constant measures the asymmetry of the two frequencies in the 2D Dunkl model. Therefore, the Hamiltonian [Formula: see text] can be interpreted as an anisotropic generalization of the curved Higgs–Dunkl oscillator in the limit [Formula: see text]. When [Formula: see text], the system turns out to be the well-known superintegrable 1:2 Dunkl oscillator on [Formula: see text] and [Formula: see text]. In this way, the integrals of the motion arising from the anisotropic Dunkl oscillator are quadratic in the Dunkl derivatives for the special cases of [Formula: see text]. Moreover, these symmetries obtain by the Jordan–Schwinger representation in the family of the Cayley–Klein orthogonal algebras using the creation and annihilation operators of the dynamical [Formula: see text] algebra of the 1D Dunkl oscillator. The resulting algebra is a deformation of [Formula: see text] with reflections, which is named the Jordan–Schwinger–Dunkl algebra [Formula: see text]. The spectrum of this system is determined by the separation of variables in geodesic polar coordinates, and the resulting eigenfunctions are algebraically given in terms of Jacobi polynomials.

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Behavior of a constrained particle on superintegrability of the two-dimensional complex Cayley–Klein space and its thermodynamic properties

Cited by 4 publications

References 39 publications

Superintegrability on the Dunkl oscillator model in three-Dimensional spaces of constant curvature

Superintegrability on the Dunkl oscillator model in three-Dimensional spaces of constant curvature

Superintegrability on the Dunkl oscillator model in three-dimensional spaces of constant curvature

The anisotropic Dunkl oscillator problem on the two-dimensional curved spaces

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