Instantons In A Symmetric Quartic Potential
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Quantum Physics arXiv:2603.00652 (quant-ph) [Submitted on 28 Feb 2026] Title:Instantons In A Symmetric Quartic Potential Authors:Pervez Hoodbhoy, M. Haashir Ismail, M. Mufassir View a PDF of the paper titled Instantons In A Symmetric Quartic Potential, by Pervez Hoodbhoy and 2 other authors View PDF HTML (experimental) Abstract:We extend the semi-classical analysis of the double-well potential to a quartic system featuring four degenerate minima. Utilizing the Feynman path integral in imaginary time, we identify longitudinal, transverse, and diagonal instanton configurations that mediate tunneling between minima. The zero mode is handled by transforming to a rotating frame whose origin lies on the classically determined path. By generalizing the dilute instanton gas approximation to account for these distinct pathways, we derive the coherent Rabi-type oscillations and the energy splittings of the four lowest-lying states. These semi-classical results are validated against high-precision numerical diagonalization, showing excellent agreement in the deep semi-classical limit. We further identify a critical coupling regime where the discrete $D_4$ symmetry undergoes a `melting' transition into a continuous $O(2)$ rotational symmetry, signaling a fundamental breakdown of the localized instanton description. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Pattern Formation and Solitons (nlin.PS); Chemical Physics (physics.chem-ph) Cite as: arXiv:2603.00652 [quant-ph] (or arXiv:2603.00652v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.00652 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Pervez Hoodbhoy [view email] [v1] Sat, 28 Feb 2026 13:44:21 UTC (1,156 KB) Full-text links: Access Paper: View a PDF of the paper titled Instantons In A Symmetric Quartic Potential, by Pervez Hoodbhoy and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: hep-th math math-ph math.MP nlin nlin.PS physics physics.chem-ph 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?)