Resonant delay in a stationary quantum clock: Lifting the threshold mask
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Quantum Physics arXiv:2606.02718 (quant-ph) [Submitted on 1 Jun 2026] Title:Resonant delay in a stationary quantum clock: Lifting the threshold mask Authors:Paul C. W. Davies, Damien A. Easson View a PDF of the paper titled Resonant delay in a stationary quantum clock: Lifting the threshold mask, by Paul C. W. Davies and Damien A. Easson View PDF HTML (experimental) Abstract:Quantum transit times have a long history of inequivalent definitions, including phase times, dwell times, and quantum-clock constructions. In this context we revisit the Salecker--Wigner--Peres stationary quantum clock as a phase-sensitive scattering observable, with clock time defined by the energy derivative of the transmission phase shift across the interaction region. For real compactly supported one-dimensional potentials, we show that the raw stationary Peres clock generically contains a universal \(1/\sqrt{E}\) continuum-edge term whose coefficient is fixed by low-energy scattering data. For the attractive square well, this threshold singularity is inherited from the vanishing exterior momentum and the associated scattering matching, rather than from resonant delay itself. We derive the exact stationary clock time for the square well and introduce a new threshold-subtracted clock observable. Away from exceptional zero-energy tuning, the subtraction removes the universal low-energy term and isolates the resonant contribution. Comparison with the dwell time and the transmission Wigner phase delay shows that the threshold-subtracted clock acquires the expected local Lorentzian form near isolated transmission resonances. Near the continuum edge, if \(\varepsilon\) denotes the detuning from threshold, the resonant peak grows only as \(\varepsilon^{-1/2}\), whereas the unsubtracted threshold background grows as \(\varepsilon^{-3/2}\). A symmetric barrier--well--barrier cavity and a numerical asymmetric two-step attractive well provide complementary controls. The result is a new threshold-subtracted stationary-clock candidate that separates universal threshold kinematics from pole-sensitive resonant delay. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) Cite as: arXiv:2606.02718 [quant-ph] (or arXiv:2606.02718v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.02718 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Damien A. Easson [view email] [v1] Mon, 1 Jun 2026 18:00:05 UTC (61 KB) Full-text links: Access Paper: View a PDF of the paper titled Resonant delay in a stationary quantum clock: Lifting the threshold mask, by Paul C. W. Davies and Damien A. EassonView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: hep-th 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?)