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Quantum tunneling, global phases and the limits of classical action reconstructions

arXiv Quantum Physics
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Physicists Chong Qi and Mário Amaro challenge a recent claim that Schrödinger wave functions can be exactly reconstructed from classical action branches without semiclassical approximations, finding critical limitations in quantum tunneling scenarios. The study reveals that classical action reconstructions fail in classically forbidden regions—like potential barriers—where real-valued action ceases to exist, requiring either complex action or a quantum potential to describe tunneling accurately. Using alpha decay and nuclear fusion models, the authors demonstrate that barrier transmission depends on global boundary conditions, which cannot emerge from local classical trajectories alone, undermining purely classical interpretations. Global quantum phase phenomena—Berry phases, flux quantization, and Josephson tunneling—further expose flaws in local action-based reconstructions, as these effects impose nonlocal phase constraints absent in classical frameworks. The findings highlight fundamental gaps in bridging classical and quantum descriptions, emphasizing the necessity of quantum corrections even in seemingly classical reconstruction attempts.
Quantum tunneling, global phases and the limits of classical action reconstructions

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Quantum Physics arXiv:2605.11252 (quant-ph) [Submitted on 11 May 2026] Title:Quantum tunneling, global phases and the limits of classical action reconstructions Authors:Chong Qi, Mário B. Amaro View a PDF of the paper titled Quantum tunneling, global phases and the limits of classical action reconstructions, by Chong Qi and M\'ario B. Amaro View PDF HTML (experimental) Abstract:It was proposed recently that the Schrödinger wave function can be reconstructed exactly from a discrete superposition of classical action branches weighted by associated classical densities, without semiclassical approximations. We examine this construction for quantum tunneling through finite potential barriers and for quantum phase phenomena. Although formally consistent when the Hamilton-Jacobi equation admits globally defined real branches, the construction breaks down in classically forbidden regions where no real classical action exists. Using rectangular and Coulomb barrier tunneling in alpha decay and nuclear fusion, we show that the wave function requires either a non-vanishing quantum potential or complex-valued action. The growing barrier component fixed by global boundary conditions is essential for transmission and cannot arise from local real classical trajectories alone. Berry phase, flux quantization, Josephson tunneling, and dc SQUID interference likewise impose global phase constraints absent from local classical action transport. Subjects: Quantum Physics (quant-ph); Superconductivity (cond-mat.supr-con); Nuclear Theory (nucl-th) Cite as: arXiv:2605.11252 [quant-ph] (or arXiv:2605.11252v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.11252 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Chong Qi [view email] [v1] Mon, 11 May 2026 21:22:10 UTC (18 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum tunneling, global phases and the limits of classical action reconstructions, by Chong Qi and M\'ario B. AmaroView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cond-mat cond-mat.supr-con nucl-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?) 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?)

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Source: arXiv Quantum Physics