Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physica Scripta

Algebraic analysis of the two-dimensional Higgs oscillator and nonlinear coherent states

V. Chithiika Ruby, M. Lakshmanan

Published Sep 1, 2025• 1 citation
Publisher

Abstract

Abstract The two-dimensional Higgs oscillator, defined on the surface of a sphere S 2 , can be mapped via a stereographic projection to a conformally transformed harmonic oscillator on the complex plane. Its quantum mechanical exact solvability provides the foundation for subsequent analyses, including the study of dual SUSY partners and the construction of continuous-variable quantum states. Due to the non-standard form of its Hamiltonian, factorization is complex, and the corresponding ladder operators are deformed. Furthermore, algebraic analysis reveals that the system satisfies the su(1, 1) algebra, which allows for the construction of Perelomov and Barut-Girardello nonlinear coherent states.

DOI
10.1088/1402-4896/ae06da

Related papers

Curvature-induced modifications in the algebraic structure of the two-dimensional Mathews–Lakshmanan nonlinear oscillator and the associated coherent states

V. Chithiika Ruby, M. Lakshmanan

Abstract The two-dimensional Mathews–Lakshmanan oscillator, which can be viewed as the planar representation of a harmonic oscillator on a space of constant curvature expressed in Euclidean coordinates, is characterized by a non-standard Hamiltonian. And it can be equivalently interpreted as a position-dependent mass system. Its quantum counterpart is exactly solvable. In this paper, we factorize the associated Hamiltonian and construct the corresponding deformed ladder operators, which do annihilation and creation operations on the eigenstates of the system and also relate them with the eigenstates of the superpartners. We analyze the shape-invariance property of the supersymmetric partner potentials and identify the underlying algebra that leads to the construction of the nonlinear coherent states for the system.

Physica Scripta•Jul 27, 2026•0 citations

Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator

Ali Mahdifar, R. Roknizadeh, M. H. Naderi

In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using non-linear coherent states approach. For this purpose, we study two-dimensional harmonic oscillators on the flat surface and on a sphere by applying the Higgs modell. With the use of their algebras, we show that the two-dimensional oscillator algebra on a surface can be considered as a deformed one-dimensional oscillator algebra where the effect of the curvature of the surface is appeared as a deformation function. We also show that the curvature of the physical space plays the role of deformation parameter. Then we construct the associated coherent states on the flat surface and on a sphere and compare their quantum statistical properties, including quadrature squeezing and antibunching effect.

•Apr 24, 2006•26 citations

Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator

A Mahdifar, R Roknizadeh, M H Naderi

In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using the nonlinear coherent states approach. For this purpose, we study two-dimensional harmonic oscillators on the flat surface and on a sphere by applying the Higgs model. With the use of their algebras, we show that the two-dimensional oscillator algebra on a surface can be considered as a deformed one-dimensional oscillator algebra where the effect of the curvature of the surface appears as a deformation function. We also show that the curvature of the physical space plays the role of deformation parameter. Then we construct the associated coherent states on the flat surface and on a sphere and compare their quantum statistical properties, including quadrature squeezing and antibunching effect.

arXiv:quant-ph/0604176•Journal of Physics A Mathematical and General•May 16, 2006•40 citations

EXACT SOLUTIONS, LADDER OPERATORS AND BARUT–GIRARDELLO COHERENT STATES FOR A HARMONIC OSCILLATOR PLUS AN INVERSE SQUARE POTENTIAL

Shi‐Hai Dong, Marcelo Lozada‐Cassou

We present exact solutions of the one-dimensional Schrödinger equation with a harmonic oscillator plus an inverse square potential. The ladder operators are constructed by the factorization method. We find that these operators satisfy the commutation relations of the generators of the dynamical group SU(1, 1). Based on those ladder operators, we obtain the analytical expressions of matrix elements for some related functions ρ and [Formula: see text] with ρ=x2. Finally, we make some comments on the Barut–Girardello coherent states and the hidden symmetry between E(x) and E(ix) by substituting x→ix.

International Journal of Modern Physics B•Nov 10, 2005•17 citations

Coherent states on a circle: The Higgs-like approach

Ali Mahdifar, Ehsan Amooghorban

In this paper, the Higgs-like approach is used to analyze the quantum dynamics of a harmonic oscillator constrained on a circle. We obtain the Hamiltonian of this system as a function of the Cartesian coordinate of the tangent line through the gnomonic projection and then quantize it in the standard way. We then recast the Hamiltonian in a shape-invariant form and derive the spectrum energy of the confined harmonic oscillator on the circle. With help of the f-deformed oscillator algebra, we construct the coherent states on the circle and investigate their quantum statistical properties. We find that such states show nonclassical features like squeezing and sub-Poissonian statistics even in small curvatures of the circle.

arXiv:2109.02251•International Journal of Geometric Methods in Modern Physics•May 4, 2022•6 citations

Aspects of coherent states of nonlinear algebras

T. Shreecharan, K. V. S. Shiv Chaitanya

Various aspects of coherent states of nonlinear su(2) and su(1, 1) algebras are studied. It is shown that the nonlinear su(1, 1) Barut–Girardello and Perelomov coherent states are related by a Laplace transform. We then concentrate on the derivation and analysis of the statistical and geometrical properties of these states. The Berry's phase for the nonlinear coherent states is also derived.

arXiv:1005.5607•Journal of Mathematical Physics•Dec 1, 2010•2 citations
Abstract The two-dimensional Higgs oscillator, defined on the surface of a sphere S 2 , can be mapped via a stereographic projection to a conformally transformed harmonic oscillator on the complex plane. Its quantum mechanical exact solvability provides the foundation for subsequent analyses, including the study of dual SUSY partners and the construction of continuous-variable quantum states. Due to the non-standard form of its Hamiltonian, factorization is complex, and the corresponding ladder operators are deformed. Furthermore, algebraic analysis reveals that the system satisfies the su(1, 1) algebra, which allows for the construction of Perelomov and Barut-Girardello nonlinear coherent states.
Abstract The two-dimensional Mathews–Lakshmanan oscillator, which can be viewed as the planar representation of a harmonic oscillator on a space of constant curvature expressed in Euclidean coordinates, is characterized by a non-standard Hamiltonian. And it can be equivalently interpreted as a position-dependent mass system. Its quantum counterpart is exactly solvable. In this paper, we factorize the associated Hamiltonian and construct the corresponding deformed ladder operators, which do annihilation and creation operations on the eigenstates of the system and also relate them with the eigenstates of the superpartners. We analyze the shape-invariance property of the supersymmetric partner potentials and identify the underlying algebra that leads to the construction of the nonlinear coherent states for the system.
In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using non-linear coherent states approach. For this purpose, we study two-dimensional harmonic oscillators on the flat surface and on a sphere by applying the Higgs modell. With the use of their algebras, we show that the two-dimensional oscillator algebra on a surface can be considered as a deformed one-dimensional oscillator algebra where the effect of the curvature of the surface is appeared as a deformation function. We also show that the curvature of the physical space plays the role of deformation parameter. Then we construct the associated coherent states on the flat surface and on a sphere and compare their quantum statistical properties, including quadrature squeezing and antibunching effect.
In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using the nonlinear coherent states approach. For this purpose, we study two-dimensional harmonic oscillators on the flat surface and on a sphere by applying the Higgs model. With the use of their algebras, we show that the two-dimensional oscillator algebra on a surface can be considered as a deformed one-dimensional oscillator algebra where the effect of the curvature of the surface appears as a deformation function. We also show that the curvature of the physical space plays the role of deformation parameter. Then we construct the associated coherent states on the flat surface and on a sphere and compare their quantum statistical properties, including quadrature squeezing and antibunching effect.
We present exact solutions of the one-dimensional Schrödinger equation with a harmonic oscillator plus an inverse square potential. The ladder operators are constructed by the factorization method. We find that these operators satisfy the commutation relations of the generators of the dynamical group SU(1, 1). Based on those ladder operators, we obtain the analytical expressions of matrix elements for some related functions ρ and [Formula: see text] with ρ=x2. Finally, we make some comments on the Barut–Girardello coherent states and the hidden symmetry between E(x) and E(ix) by substituting x→ix.
In this paper, the Higgs-like approach is used to analyze the quantum dynamics of a harmonic oscillator constrained on a circle. We obtain the Hamiltonian of this system as a function of the Cartesian coordinate of the tangent line through the gnomonic projection and then quantize it in the standard way. We then recast the Hamiltonian in a shape-invariant form and derive the spectrum energy of the confined harmonic oscillator on the circle. With help of the f-deformed oscillator algebra, we construct the coherent states on the circle and investigate their quantum statistical properties. We find that such states show nonclassical features like squeezing and sub-Poissonian statistics even in small curvatures of the circle.