A Generalization of the Parametric Amplifier with Dunkl Derivative: Spectral and Statistical Properties
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Quantum Physics arXiv:2602.16743 (quant-ph) [Submitted on 18 Feb 2026] Title:A Generalization of the Parametric Amplifier with Dunkl Derivative: Spectral and Statistical Properties Authors:D. Ojeda Guillén, R. D. Mota, J. C. Vega View a PDF of the paper titled A Generalization of the Parametric Amplifier with Dunkl Derivative: Spectral and Statistical Properties, by D. Ojeda Guill\'en and 1 other authors View PDF HTML (experimental) Abstract:We study the parametric amplifier Hamiltonian within the framework of the Dunkl formalism. We introduce the Dunkl creation and annihilation operators and show that their quadratic combinations generate an $su(1,1)$ Lie algebra. The spectral problem is solved exactly using two algebraic methods: the $su(1,1)$ tilting transformation and the generalized Bogoliubov transformation. The exact energy spectrum and the corresponding eigenfunctions are obtained in terms of the Dunkl number coherent states. Furthermore, we compute the Mandel $Q$ parameter and the second-order correlation function $g^{(2)}(0)$ to analyze the statistical properties of the Dunkl squeezed states. We show that, for the squeezed vacuum, the Mandel parameter remains independent of the Dunkl deformation, whereas the correlation function exhibits an explicit dependence on the Dunkl parameter $\mu$, which modifies the photon bunching effects. Finally, we show that our results reduce to the standard parametric amplifier case in the limit of vanishing Dunkl deformation parameter. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2602.16743 [quant-ph] (or arXiv:2602.16743v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.16743 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Didier Ojeda-Guillén [view email] [v1] Wed, 18 Feb 2026 02:46:00 UTC (14 KB) Full-text links: Access Paper: View a PDF of the paper titled A Generalization of the Parametric Amplifier with Dunkl Derivative: Spectral and Statistical Properties, by D. Ojeda Guill\'en and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)