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

$(q;l,\\lambda)$-Deformed Heisenberg Algebra: Coherent States, Their Statistics and Geometry

J. D. Bukweli-Kyemba, Mahouton Norbert Hounkonnou

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

The Heisenberg algebra is deformed with the set of parameters $\\{q, l,\\lambda\\}$ to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly computed. Then, a proof on the subPoissonian character of the statistics of the main deformed states is provided. This property is used to determine the induced generalized metric.

Related papers

$(q;l,λ)$-deformed Heisenberg algebra: coherent states, their statistics and geometry

Joseph Désiré Bukweli, Mahouton Norbert Hounkonnou

The Heisenberg algebra is deformed with the set of parameters ${q, l,λ}$ to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly computed. Then, a proof on the sub-Poissonian character of the statistics of the main deformed states is provided. This property is used to determine the induced generalized metric.

arXiv:1211.3312•Nov 14, 2012•0 citations

Quantum deformed algebras : Coherent states and special functions

J. D. Bukweli-Kyemba, Mahouton Norbert Hounkonnou

The Heisenberg algebra is first deformed with the set of parameters ${q, l, λ}$ to generate a new family of generalized coherent states. In this framework, the matrix elements of relevant operators are exactly computed. A proof on sub-Poissonian character of the statistics of the main deformed states is provided. This property is used to determine a generalized metric. A unified method of calculating structure functions from commutation relations of deformed single-mode oscillator algebras is then presented. A natural approach to building coherent states associated to deformed algebras is deduced. Known deformed algebras are given as illustration. Futhermore, we generalize a class of two-parameter deformed Heisenberg algebras related to meromorphic functions, called ${\cal R}(p,q)$-deformed algebra. Relevant families of coherent states maps are probed and their corresponding hypergeometric series are computed. The latter generalizes known hypergeometric series and gives to a generalization of the binomial theorem. The involved notions of differentiation and integration generalize the usual $q$- and $(p,q)$-differentiation and integration. A Hopf algebra structure compatible with the ${\cal R}(p,q)$-algebra is deduced. We succeed in giving a new characterization of Rogers- Szegö polynomials, called ${\cal R}(p,q)$-deformed Rogers-Szegö polynomials, by their three-term recursion relations and the associated quantum algebra built with corresponding creation and annihilation operators. Continuous ${\cal R}(p,q)$-deformed Hermite polynomials and their recursion relation are also deduced. Novel algebraic relations are provided and discussed. The whole formalism is performed in a unified way, generalizing known relevant results which are straightforwardly derived as particular cases.

arXiv:1301.0116•Jan 1, 2013•14 citations

$(q;l,λ)-$deformed Heisenberg algebra: representations, special functions and quantization

Mahouton Norbert Hounkonnou, Sama Arjika, Ezinvi Baloïtcha

This paper addresses a new characterization of Sudarshan's diagonal representation of the density matrix elements $ρ(z',z)$, derivedfrom $(q;l,λ)-$deformed boson coherent states.The induced $ρ(z',z)$ self-reproducing property with the associated self-reproducing kernel $K(z',z)$ is computed and analyzed. An explicit construction of novel classes of generalized continuous $(q;l,λ)-$Hermite polynomials is provided with the corresponding recursion relations and exact resolution of the moment problems giving their orthogonality weight functions. Besides, the Berezin-Klauder-Toeplitz quantization of classical phase space observables and relevant normal and anti-normal forms are investigated and discussed.

arXiv:1301.7028•Jan 29, 2013•0 citations

COHERENT STATE OF α-DEFORMED WEYL–HEISENBERG ALGEBRA

Sh. Dehdashti, Ali Mahdifar, R. Roknizadeh

At first, we introduce α-deformed algebra as a kind of generalization of the Weyl–Heisenberg algebra so that we get the su(2)- and su(1, 1)-algebras whenever α has specific values. After that, we construct coherent states of this algebra. Third, a realization of this algebra is given in the system of a harmonic oscillator confined at the center of a potential well. Then, we introduce two-boson realization of the α-deformed Weyl–Heisenberg algebra and use this representation to write α-deformed coherent states in terms of the two modes number states. Following these points, we consider mean number of excitations (we call them in general photons) and Mandel parameter as statistical properties of the α-deformed coherent states. Finally, the Fubini–Study metric is calculated for the α-coherent states manifold.

International Journal of Geometric Methods in Modern Physics•Feb 7, 2013•11 citations

New Deformation of quantum oscillator algebra: Representation and some application

Sama Arjika, Dine Ousmane Samary, Ezinvi Baloïtcha +1 more

This work addresses the study of the oscillator algebra, defined by four parameters $p$, $q$, $α$, and $ν$. The time-independent Schrödinger equation for the induced deformed harmonic oscillator is solved; explicit analytic expressions of the energy spectrum are given. Deformed states are built and discussed with respect to the criteria of coherent state construction. Various commutators involving annihilation and creation operators and their combinatorics are computed and analyzed. Finally, the correlation functions of matrix elements of main normal and antinormal forms, pertinent for quantum optics analysis, are computed.

arXiv:1210.7259•Oct 26, 2012•0 citations

Gazeau-Klauder coherent states in position-deformed Heisenberg algebra

Latévi M. Lawson, Prince K. Osei

Abstract In this paper, we present coherent states à la Gazeau-Klauder for a free particle in square well potential within position-deformed Heisenberg algebra . These states satisfy the Klauder’s mathematical requirement to build coherent states. Some statistical properties such as the probability distribution, the intensity correlation function and the Mandel parameter are calculated and analyzed. We find that these states are sub-Poissonian in nature. We also construct for these coherent states, the even cat states and we evaluate its Wigner function which analyses the quasiprobability distribution of these states. We graphically demonstrate that these states exhibit nonclassical behavior.

Journal of Physics Communications•Aug 1, 2022•4 citations
(q;l,lambda)(q;l,\\lambda)(q;l,lambda)-Deformed Heisenberg Algebra: Coherent States, Their Statistics and Geometry
The Heisenberg algebra is deformed with the set of parameters q,l,lambda\\{q, l,\\lambda\\}q,l,lambda to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly computed. Then, a proof on the subPoissonian character of the statistics of the main deformed states is provided. This property is used to determine the induced generalized metric.
(q;l,λ)(q;l,λ)(q;l,λ)-deformed Heisenberg algebra: coherent states, their statistics and geometry
The Heisenberg algebra is deformed with the set of parameters q,l,λ{q, l,λ}q,l,λ to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly computed. Then, a proof on the sub-Poissonian character of the statistics of the main deformed states is provided. This property is used to determine the induced generalized metric.
The Heisenberg algebra is first deformed with the set of parameters q,l,λ{q, l, λ}q,l,λ to generate a new family of generalized coherent states. In this framework, the matrix elements of relevant operators are exactly computed. A proof on sub-Poissonian character of the statistics of the main deformed states is provided. This property is used to determine a generalized metric. A unified method of calculating structure functions from commutation relations of deformed single-mode oscillator algebras is then presented. A natural approach to building coherent states associated to deformed algebras is deduced. Known deformed algebras are given as illustration. Futhermore, we generalize a class of two-parameter deformed Heisenberg algebras related to meromorphic functions, called R(p,q){\cal R}(p,q)R(p,q)-deformed algebra. Relevant families of coherent states maps are probed and their corresponding hypergeometric series are computed. The latter generalizes known hypergeometric series and gives to a generalization of the binomial theorem. The involved notions of differentiation and integration generalize the usual qqq- and (p,q)(p,q)(p,q)-differentiation and integration. A Hopf algebra structure compatible with the R(p,q){\cal R}(p,q)R(p,q)-algebra is deduced. We succeed in giving a new characterization of Rogers- Szegö polynomials, called R(p,q){\cal R}(p,q)R(p,q)-deformed Rogers-Szegö polynomials, by their three-term recursion relations and the associated quantum algebra built with corresponding creation and annihilation operators. Continuous R(p,q){\cal R}(p,q)R(p,q)-deformed Hermite polynomials and their recursion relation are also deduced. Novel algebraic relations are provided and discussed. The whole formalism is performed in a unified way, generalizing known relevant results which are straightforwardly derived as particular cases.
(q;l,λ)−(q;l,λ)-(q;l,λ)−deformed Heisenberg algebra: representations, special functions and quantization
This paper addresses a new characterization of Sudarshan's diagonal representation of the density matrix elements ρ(z′,z)ρ(z',z)ρ(z′,z), derivedfrom (q;l,λ)−(q;l,λ)-(q;l,λ)−deformed boson coherent states.The induced ρ(z′,z)ρ(z',z)ρ(z′,z) self-reproducing property with the associated self-reproducing kernel K(z′,z)K(z',z)K(z′,z) is computed and analyzed. An explicit construction of novel classes of generalized continuous (q;l,λ)−(q;l,λ)-(q;l,λ)−Hermite polynomials is provided with the corresponding recursion relations and exact resolution of the moment problems giving their orthogonality weight functions. Besides, the Berezin-Klauder-Toeplitz quantization of classical phase space observables and relevant normal and anti-normal forms are investigated and discussed.
At first, we introduce α-deformed algebra as a kind of generalization of the Weyl–Heisenberg algebra so that we get the su(2)- and su(1, 1)-algebras whenever α has specific values. After that, we construct coherent states of this algebra. Third, a realization of this algebra is given in the system of a harmonic oscillator confined at the center of a potential well. Then, we introduce two-boson realization of the α-deformed Weyl–Heisenberg algebra and use this representation to write α-deformed coherent states in terms of the two modes number states. Following these points, we consider mean number of excitations (we call them in general photons) and Mandel parameter as statistical properties of the α-deformed coherent states. Finally, the Fubini–Study metric is calculated for the α-coherent states manifold.
This work addresses the study of the oscillator algebra, defined by four parameters ppp, qqq, ααα, and ννν. The time-independent Schrödinger equation for the induced deformed harmonic oscillator is solved; explicit analytic expressions of the energy spectrum are given. Deformed states are built and discussed with respect to the criteria of coherent state construction. Various commutators involving annihilation and creation operators and their combinatorics are computed and analyzed. Finally, the correlation functions of matrix elements of main normal and antinormal forms, pertinent for quantum optics analysis, are computed.
Abstract In this paper, we present coherent states à la Gazeau-Klauder for a free particle in square well potential within position-deformed Heisenberg algebra . These states satisfy the Klauder’s mathematical requirement to build coherent states. Some statistical properties such as the probability distribution, the intensity correlation function and the Mandel parameter are calculated and analyzed. We find that these states are sub-Poissonian in nature. We also construct for these coherent states, the even cat states and we evaluate its Wigner function which analyses the quasiprobability distribution of these states. We graphically demonstrate that these states exhibit nonclassical behavior.