Bound states and decay dynamics in $N$-level Friedrichs model with factorizable interactions

Quantum Physics arXiv:2512.17207 (quant-ph) [Submitted on 19 Dec 2025] Title:Bound states and decay dynamics in $N$-level Friedrichs model with factorizable interactions Authors:Jia-Ming Zhang, Yu Xin, Bing Chen View a PDF of the paper titled Bound states and decay dynamics in $N$-level Friedrichs model with factorizable interactions, by Jia-Ming Zhang and 2 other authors View PDF HTML (experimental) Abstract:Considering an $N$-level system interacting factorizably with a continuous spectrum, we derive analytical expressions for the bound states and the dynamical evolution within this single-excitation Friedrichs model by using the projection operator formalism. First, we establish explicit criteria to determine the number of bound states, whose existence suppresses the complete spontaneous decay of the system. Second, we derive the open system's dissipative dynamics, which is naturally described by an energy-independent non-Hermitian Hamiltonian in the Markovian limit. As an example, we apply our framework to an atomic chain embedded in a photonic crystal waveguide, uncovering a rich variety of decay dynamics and realizing an anti-$\mathcal{PT}$-symmetric Hamiltonian in the system's evolution. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2512.17207 [quant-ph] (or arXiv:2512.17207v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.17207 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jia-Ming Zhang [view email] [v1] Fri, 19 Dec 2025 03:37:36 UTC (322 KB) Full-text links: Access Paper: View a PDF of the paper titled Bound states and decay dynamics in $N$-level Friedrichs model with factorizable interactions, by Jia-Ming Zhang and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 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?)