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 -deformati...

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Bibliographic Details
Published in:Letters in mathematical physics 2021-12, Vol.111 (6), Article 143
Main Authors: Mouayn, Zouhaïr, El Moize, Othmane
Format: Article
Language:English
Subjects:
Complex Systems
Deformation
Generalized Arik-Coon spaces
Geometry
Group Theory and Generalizations
Harmonic oscillators
Hermite polynomials
Mathematical and Computational Physics
Physics
Physics and Astronomy
q-coherent states
q-deformed 2D complex Hermite polynomials
q-deformed Bargmann transform
Reproducing kernels
Rogers-Szego oscillator
Theoretical
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Summary: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.
ISSN:0377-9017
1573-0530
1573-0530
DOI:10.1007/s11005-021-01486-y