Immiscible to miscible quenching instabilities in two-dimensional binary Bose-Einstein condensates

Immiscible to miscible quenching instabilities in two-dimensional binary Bose-Einstein condensates | 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 Immiscible to miscible quenching instabilities in two-dimensional binary Bose-Einstein condensates LAURO TOMIO, Subramaniyan Sabari, Arnaldo Gammal, Kishor Ramavarmaraja Kumar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8408106/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract Immiscible to miscible quenching transitions (IMQT) in homogeneous Bose-Einstein condensate are investigated, considering rubidium isotopes $^{85}$Rb and $^{87}$Rbconfined in a two-dimensional (2D) circular box, under two different initial configurations. These IMQT instabilities, triggered by sudden reductions in the two-body interspecies scattering length $a_{12}$, are explored under two distinct initialconditions, highlighting the critical role of nonlinear dynamics in their evolution. The numerical simulations indicate that the instability dynamics are primarily driven by the production of large vortices and the propagation of sound waves (phonons), with sound wave excitations prevailing in the long-term evolution. The compressible and incompressible parts of the kinetic energy spectra, in terms of the wave number $k$, are confronted with the classical Kolmogorov scaling, $k^{-5/3}$ for turbulence, which is observed in the onset of instabilities. Before reaching the ultraviolet dissipation region at small scales, the IMQT spectra exhibit a bottleneck effect, indicating a clear departure from classical scaling behavior. In the time asymptotic miscible regime, it is observed that the vorticity and sound-wave production remain practically stable. In this regime, for both cases investigated, a linear relation is also recognized between the miscibility parameter and the initial IMQT configuration. Bose-Einstein condensate Kolmogorov vorticity nonlinear waves Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 15 Apr, 2026 Reviews received at journal 14 Apr, 2026 Reviewers agreed at journal 25 Mar, 2026 Reviewers agreed at journal 17 Jan, 2026 Reviewers invited by journal 30 Dec, 2025 Editor assigned by journal 22 Dec, 2025 Submission checks completed at journal 20 Dec, 2025 First submitted to journal 19 Dec, 2025 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8408106","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":567257622,"identity":"0015c42d-3567-4f79-9b5e-2820e169228b","order_by":0,"name":"LAURO TOMIO","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYBACPjiLmYHxAZDi4cOpFgrYIJQBSAuzAUgLG/FagGwJJBE8WtjPmH34wPBHTred+Vjl1xw7GTYG5oePbuDTwpNjPHMGg4Gx2WG2tNuy25KBDmMzNs7B67AcY2YeBoPEbYd5zG5LbmMGauFhk8arhf8NQkux5LZ6IrRIINnC+BFIEqHlWTHjDANjkF+SpRm3HedhYybgF37+5M0MHyrk5MzOHz748ee2ant+9uaHj/FpgQADCAV0IYgkqBwJMP4gRfUoGAWjYBSMGAAAMrM3tqHEU4wAAAAASUVORK5CYII=","orcid":"","institution":"São Paulo State University","correspondingAuthor":true,"prefix":"","firstName":"LAURO","middleName":"","lastName":"TOMIO","suffix":""},{"id":567257623,"identity":"ba68c60b-d7ed-4721-95d3-53ad68cb7afc","order_by":1,"name":"Subramaniyan Sabari","email":"","orcid":"","institution":"São Paulo State University","correspondingAuthor":false,"prefix":"","firstName":"Subramaniyan","middleName":"","lastName":"Sabari","suffix":""},{"id":567257625,"identity":"3a92e03b-e710-4905-be85-36171be7c4b5","order_by":2,"name":"Arnaldo Gammal","email":"","orcid":"","institution":"Universidade de São Paulo","correspondingAuthor":false,"prefix":"","firstName":"Arnaldo","middleName":"","lastName":"Gammal","suffix":""},{"id":567257627,"identity":"506cf2d7-bf5d-4ca5-b11c-2b470e5ca331","order_by":3,"name":"Kishor Ramavarmaraja Kumar","email":"","orcid":"","institution":"São Paulo State University","correspondingAuthor":false,"prefix":"","firstName":"Kishor","middleName":"Ramavarmaraja","lastName":"Kumar","suffix":""}],"badges":[],"createdAt":"2025-12-19 20:53:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8408106/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8408106/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99337793,"identity":"ca00b886-f7ab-4a26-b7c6-24c0436a8833","added_by":"auto","created_at":"2026-01-01 03:24:55","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5868,"visible":true,"origin":"","legend":"","description":"","filename":"a7e4bf3d8761479fbfb0de1e67d6142e.json","url":"https://assets-eu.researchsquare.com/files/rs-8408106/v1/79e2376d9932b762900b34f4.json"},{"id":99788758,"identity":"1cba0616-afab-4e19-9e07-6b60ded03276","added_by":"auto","created_at":"2026-01-08 12:47:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":821660,"visible":true,"origin":"","legend":"","description":"","filename":"TOMIOAPFB2025FBSIMQT.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8408106/v1_covered_a95a5051-7dea-4231-9f98-8b99ba60ea3c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Immiscible to miscible quenching instabilities in two-dimensional binary Bose-Einstein condensates","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"few-body-systems","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"fbsy","sideBox":"Learn more about [Few-Body Systems](http://link.springer.com/journal/601)","snPcode":"601","submissionUrl":"https://submission.nature.com/new-submission/601/3","title":"Few-Body Systems","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Bose-Einstein condensate, Kolmogorov, vorticity, nonlinear waves","lastPublishedDoi":"10.21203/rs.3.rs-8408106/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8408106/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Immiscible to miscible quenching transitions (IMQT) in homogeneous Bose-Einstein condensate are investigated, considering rubidium isotopes $^{85}$Rb and $^{87}$Rbconfined in a two-dimensional (2D) circular box, under two different initial configurations. These IMQT instabilities, triggered by sudden reductions in the two-body interspecies scattering length $a_{12}$, are explored under two distinct initialconditions, highlighting the critical role of nonlinear dynamics in their evolution. The numerical simulations indicate that the instability dynamics are primarily driven by the production of large vortices and the propagation of sound waves (phonons), with sound wave excitations prevailing in the long-term evolution. The compressible and incompressible parts of the kinetic energy spectra, in terms of the wave number $k$, are confronted with the classical Kolmogorov scaling, $k^{-5/3}$ for turbulence, which is observed in the onset of instabilities. Before reaching the ultraviolet dissipation region at small scales, the IMQT spectra exhibit a bottleneck effect, indicating a clear departure from classical scaling behavior. In the time asymptotic miscible regime, it is observed that the vorticity and sound-wave production remain practically stable. 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