Numerical simulations of superfluid 3He

Numerical simulations of superfluid 3He | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Numerical simulations of superfluid 3 He Asier Lopez-Eiguren, Mark Hindmarsh, Kari Rummukainen, Kuang Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8844655/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 13 You are reading this latest preprint version Abstract The first-order phase transition between the supercooled A- and B-phase in superfluid 3He at millikelvin temperatures remains a long-standing puzzle. While homogeneous nucleation (HN) theory predicts an almost negligible transition rate, experiments observe A-phase lifetimes ranging from hours to days, indicating a highly non-equilibrium process. Various mechanisms,including the “baked-Alaska” model and the “cosmological” scenario, have been proposed to explain this discrepancy, with broader implications for cosmological phase transitions and dark matter models. Recent experiments have revealed new properties of this transition, emphasizing the need to understand the superfluid phase seeding, the post-seeding evolution of the order parameter and the influence of container boundaries on A-phase stability. To address this challenge, we present dyGiLa, a massively parallel code for lattice simulationsof superfluid 3He. Built using computational techniques originally developed for cosmological field theory simulations, dyGiLa solves the effective field theory of the superfluid order parameter by integrating the time-dependent Ginzburg-Landau equations on large-scale cuboidal grids, constrained only by available computational resources. This transfer of technology from cosmology enables efficient and scalable simulations of complex non-equilibrium dynamics in p-wave superfluid 3He. We demonstrate results from rapid quench simulations, showcasing the emergence of diverse topological defects and phase boundaries. DyGiLa is currently being employed to interpret experimental findings from the QUEST-DMC collaboration, providing new insights into the intricate dynamics of the AB transition. helium 3 phase transitions time-dependent Ginzburg-Landau equation cosmology early universe gravitational waves Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 30 Mar, 2026 Reviews received at journal 25 Mar, 2026 Reviews received at journal 24 Mar, 2026 Reviews received at journal 16 Mar, 2026 Reviewers agreed at journal 16 Mar, 2026 Reviewers agreed at journal 15 Mar, 2026 Reviewers agreed at journal 15 Mar, 2026 Reviews received at journal 13 Mar, 2026 Reviewers agreed at journal 02 Mar, 2026 Reviewers invited by journal 26 Feb, 2026 Editor assigned by journal 11 Feb, 2026 Submission checks completed at journal 11 Feb, 2026 First submitted to journal 10 Feb, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8844655","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":599548242,"identity":"01f53c6f-d1cc-4d41-a2f4-d990c0fbb3d3","order_by":0,"name":"Asier Lopez-Eiguren","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYFACxgYgYQFmPQCzidQiAWIxGxCpBQzAWtgkiNLC33+48XEFg4ScOXv7s4qPOw4z8EukP8Bv/I3EZsMzDBLGlj0H0m7OPHOYQXJGjgF+a24wtkk2MEgkbriRcOw2b9thBoMbOfh1yJ8/2P4TrOX+w7biv0At9jcIOMzgQGIbI8QWZjZmRpAtEgn4HWYI9ItkgwHIL2nMkr1t6TwSZ97g1yJ3/vjDjw0VNsAQO/7ww882azn+dgIOgzoPjMCAhwjlCF2jYBSMglEwCrADAPAlRjKQ3ntuAAAAAElFTkSuQmCC","orcid":"","institution":"University of the Basque Country","correspondingAuthor":true,"prefix":"","firstName":"Asier","middleName":"","lastName":"Lopez-Eiguren","suffix":""},{"id":599548243,"identity":"74dfb02a-c2d5-43dc-88d3-68b4a6bd32ba","order_by":1,"name":"Mark Hindmarsh","email":"","orcid":"","institution":"University of Sussex","correspondingAuthor":false,"prefix":"","firstName":"Mark","middleName":"","lastName":"Hindmarsh","suffix":""},{"id":599548244,"identity":"86c712c3-4675-400f-b34f-f4edb55ffd80","order_by":2,"name":"Kari Rummukainen","email":"","orcid":"","institution":"University of Helsinki","correspondingAuthor":false,"prefix":"","firstName":"Kari","middleName":"","lastName":"Rummukainen","suffix":""},{"id":599548246,"identity":"45d5d5ed-c25c-43b3-92f9-fe63e9c9ee6a","order_by":3,"name":"Kuang Zhang","email":"","orcid":"","institution":"University of Sussex","correspondingAuthor":false,"prefix":"","firstName":"Kuang","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2026-02-10 19:08:37","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8844655/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8844655/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104401379,"identity":"4cf257d5-5261-4663-b4eb-5fa77340eea5","added_by":"auto","created_at":"2026-03-11 12:12:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":879836,"visible":true,"origin":"","legend":"","description":"","filename":"Numericalsimulationsofsuperfluid3He.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8844655/v1_covered_f495f780-a826-4b5d-8f57-61d6d63d9122.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eNumerical simulations of superfluid \u003csup\u003e3\u003c/sup\u003eHe\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-low-temperature-physics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jltp","sideBox":"Learn more about [Journal of Low Temperature Physics](http://link.springer.com/journal/10909)","snPcode":"10909","submissionUrl":"https://submission.nature.com/new-submission/10909/3","title":"Journal of Low Temperature Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"helium 3, phase transitions, time-dependent Ginzburg-Landau equation, cosmology, early universe, gravitational waves","lastPublishedDoi":"10.21203/rs.3.rs-8844655/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8844655/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The first-order phase transition between the supercooled A- and B-phase in superfluid 3He at millikelvin temperatures remains a long-standing puzzle. While homogeneous nucleation (HN) theory predicts an almost negligible transition rate, experiments observe A-phase lifetimes ranging from hours to days, indicating a highly non-equilibrium process. Various mechanisms,including the “baked-Alaska” model and the “cosmological” scenario, have been proposed to explain this discrepancy, with broader implications for cosmological phase transitions and dark matter models. Recent experiments have revealed new properties of this transition, emphasizing the need to understand the superfluid phase seeding, the post-seeding evolution of the order parameter and the influence of container boundaries on A-phase stability. To address this challenge, we present dyGiLa, a massively parallel code for lattice simulationsof superfluid 3He. 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