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arXiv · 2102.10714

A set of $q$-coherent states for the Rogers-Szeg\H{o} oscillator

Othmane El Moize·Zouhaïr Mouayn
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Abstract

We discuss a model of a $q$-harmonic oscillator based on Rogers-Szeg\H{o} 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.

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Othmane El Moize, Zouhaïr Mouayn. 2021-02-21. A set of $q$-coherent states for the Rogers-Szeg\H{o} oscillator. https://arxiv.org/abs/2102.10714

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