We discuss a model of a $q$ -harmonic oscillator based on Rogers-Szegő functions. We combine these functions with a class of $q$ -analogs of complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative integer parameter $m$ . Our construction leads to a new $q$ -deformation of the $m$ -true-polyanalytic Bargmann transform whose range defines a generalization of the Arik-Coon space. We also give an explicit formula for the reproducing kernel of this space. The obtained results may be exploited to define a $q$ -deformation of the Ginibre- $m$ -type process on the complex plane.We discuss a model of a $q$-harmonic oscillator based on Rogers-Szegő functions. We combine these functions with a class of $q$-analogs of complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative integer parameter $m$. Our construction leads to a new $q$-deformation of the $m$-true-polyanalytic Bargmann transform whose range defines a generalization of the Arik-Coon space. We also give an explicit formula for the reproducing kernel of this space. The obtained results may be exploited to define a $q$-deformation of the Ginibre-$m$-type process on the complex plane.

arXiv:2102.10714Feb 21, 20210 citations

Coherent States of Two-Mode q-Oscillators with a q Root of Unity

Won Sang Chung

International Journal of Theoretical PhysicsOct 1, 20010 citations

Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

Marcelo A. Marchiolli, M. Ruzzi, D. Galetti

By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in details. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in details. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.

arXiv:0903.4059Mar 24, 20090 citations

Semi-coherent states of the quantum harmonic oscillator

P. M. Mathews, Kumar Eswaran

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BOct 1, 197317 citations

Algebraic properties of Rogers–Szegö functions: I. Applications in quantum optics

Marcelo A. Marchiolli, M. Ruzzi, D. Galetti

By means of a well-established algebraic framework, Rogers–Szegö functions associated with a circular geometry in the complex plane are introduced in the context of q -special functions, and their properties are discussed in detail. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers–Szegö functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson–Schrödinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q -deformed coherent states.By means of a well-established algebraic framework, Rogers–Szegö functions associated with a circular geometry in the complex plane are introduced in the context of q -special functions, and their properties are discussed in detail. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers–Szegö functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson–Schrödinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q -deformed coherent states.

Journal of Physics A Mathematical and TheoreticalAug 28, 20093 citations

A set of

q

-coherent states for the Rogers-Szegő oscillator

We discuss a model of a

q

-harmonic oscillator based on Rogers-Szegő functions. We combine these functions with a class of

q

-analogs of complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative integer parameter

m

. Our construction leads to a new

q

-deformation of the

m

-true-polyanalytic Bargmann transform whose range defines a generalization of the Arik-Coon space. We also give an explicit formula for the reproducing kernel of this space. The obtained results may be exploited to define a

q

-deformation of the Ginibre-

m

-type process on the complex plane.