Quantum Dynamics and Collapse-and-Revival Phenomena in the Dunkl Anharmonic Oscillator
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Quantum Physics arXiv:2604.22945 (quant-ph) [Submitted on 24 Apr 2026] Title:Quantum Dynamics and Collapse-and-Revival Phenomena in the Dunkl Anharmonic Oscillator Authors:D. Ojeda-Guillén, R. D. Mota, M. Salazar-Ramírez View a PDF of the paper titled Quantum Dynamics and Collapse-and-Revival Phenomena in the Dunkl Anharmonic Oscillator, by D. Ojeda-Guill\'en and 1 other authors View PDF HTML (experimental) Abstract:We study the Dunkl anharmonic oscillator (Kerr medium) Hamiltonian from an algebraic approach of the $SU(1,1)$ group. In order to obtain the exact energy spectrum of this problem, we write its Hamiltonian in terms of the Dunkl creation and annihilation operators, which close the $su(1,1)$ Lie algebra. This allows us to exactly solve this Hamiltonian and obtain its parity-dependent energy spectrum. Then, we investigate the quantum dynamics of the system, particularly the collapse and revival phenomena, by using an initial state given by a superposition of even and odd Dunkl coherent states. We compute the field quadrature and the survival probability, showing that the Dunkl parameter $\mu$ modulates the fractional revivals and produces perfect state reconstructions at half-periods for specific deformation values. We analyze the quadrature variance to show that the Dunkl deformation generates interference-induced squeezed states around $t \approx \pi$. The standard Kerr medium dynamics are exactly recovered in the limit $\mu \rightarrow 0$. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2604.22945 [quant-ph] (or arXiv:2604.22945v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.22945 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Didier Ojeda-Guillén [view email] [v1] Fri, 24 Apr 2026 18:37:30 UTC (798 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Dynamics and Collapse-and-Revival Phenomena in the Dunkl Anharmonic Oscillator, by D. Ojeda-Guill\'en and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?) 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?)