Supersymmetry of dissipative Bose-Fermi systems with application to Jaynes-Cummings and Dicke models
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Quantum Physics arXiv:2606.12682 (quant-ph) [Submitted on 10 Jun 2026] Title:Supersymmetry of dissipative Bose-Fermi systems with application to Jaynes-Cummings and Dicke models Authors:Colin V. Coane, Francesco Iachello View a PDF of the paper titled Supersymmetry of dissipative Bose-Fermi systems with application to Jaynes-Cummings and Dicke models, by Colin V. Coane and 1 other authors View PDF HTML (experimental) Abstract:We demonstrate how supersymmetries of Hamiltonians for coupled Bose-Fermi systems can be used to place the Hamiltonians of the Jaynes-Cummings model and Dicke model under the rotating wave approximation in matrix form and provide explicit analytic solutions for their eigenvalues. We then use this supersymmetry to place the Liouvillians of the associated Markovian open systems in matrix form and provide explicit solutions for their eigenvalues. These results are a consequence of the fact that the Hamiltonian of the Jaynes-Cummings model commutes with the linear Casimir invariant of the superalgebra $u(1|1)$ and that the Hamiltonian of the Dicke model commutes both with the linear invariant of $\sum_{i} u_{i}(1|1)$ and with the invariant of an additional $su(2)$ algebra. Our methods apply to various coupled Bose-Fermi systems with $u(1|1)$ and more generally with $u(n|m)$ dynamical superalgebras, and may provide efficient tools for studying more complicated examples. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2606.12682 [quant-ph] (or arXiv:2606.12682v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.12682 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Colin Coane [view email] [v1] Wed, 10 Jun 2026 21:10:36 UTC (1,665 KB) Full-text links: Access Paper: View a PDF of the paper titled Supersymmetry of dissipative Bose-Fermi systems with application to Jaynes-Cummings and Dicke models, by Colin V. Coane and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)