Dawn and Twilight Time in Quantum Tunneling
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Quantum Physics arXiv:2512.14809 (quant-ph) [Submitted on 16 Dec 2025] Title:Dawn and Twilight Time in Quantum Tunneling Authors:Tinglong Feng, Jesse Moes, Tomislav Prokopec View a PDF of the paper titled Dawn and Twilight Time in Quantum Tunneling, by Tinglong Feng and 2 other authors View PDF Abstract:Metastable decay exhibits a familiar exponential regime bracketed by early-time deviations and late-time power-law tails. We adopt the real-time, flux-based definition of the decay rate in the spirit of Andreassen et al.\ direct method and present a complete analysis of one-dimensional quantum-mechanical resonance models. We show that the kernel admits a universal pole--plus--branch decomposition and use it to define two computable time scales: a dawn time, when a single resonant contribution starts dominating and exponential decay sets in, and a twilight time, when the branch-cut tail overtakes exponential decay. The latter can be expressed in closed form via the Lambert $W$ function, making its parametric dependence manifest without fitting. For square, modified square, and Pöschl--Teller barriers we obtain simple thick-barrier formulas, clarify the relation $\Gamma T = T_{\text{trans}}$ between the decay rate $\Gamma$, oscillation period $T$, and transmission probability $T_{\text{trans}}$, and indicate how our spectral picture can be naturally extended to quantum field theoretic vacuum decay. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2512.14809 [quant-ph] (or arXiv:2512.14809v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.14809 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tinglong Feng [view email] [v1] Tue, 16 Dec 2025 18:59:39 UTC (147 KB) Full-text links: Access Paper: View a PDF of the paper titled Dawn and Twilight Time in Quantum Tunneling, by Tinglong Feng and 2 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: hep-th 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?)