One dimensional Quantum Droplets under the effect of curved space-time

One dimensional Quantum Droplets under the effect of curved space-time | 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 One dimensional Quantum Droplets under the effect of curved space-time Abdelhakim Benkrane This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7427321/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this paper, we study quantum droplets in one dimension under the influence of space-time curvature by redefining the momentum operator ˆ P = −i(1 +αx^2)∂/∂x, resulting in a maximum length and a minimum momentum, consistent with anti-de Sitter space (AdS). By analyzing this effect through the α parameter on the exact solution of free quantum droplets, we find that the relationship between the number of atoms and the chemical potential deviates from the ordinary case. Additionally, we observe that the characteristic f lat-top shape of quantum droplets can disappear, transforming into a Gaussian profile in the presence of the maximum length (minimum momentum). Furthermore, our findings reveal that the interaction of quantum droplets with space-time curvature results in an increase in their size. Finally, by studying this effect on the variational solution using a Gaussian ansatz for small droplets, we conclude that α reduces the stability and self-localization of the quantum droplets. Quantum droplets Ultra cold atoms Space-time curvature Minimal momentum Maximal length Modified Heisenberg uncertainty principle Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted 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-7427321","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":503740738,"identity":"4f870277-730b-4e95-9e64-09c747ff81b7","order_by":0,"name":"Abdelhakim Benkrane","email":"data:image/png;base64,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","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Abdelhakim","middleName":"","lastName":"Benkrane","suffix":""}],"badges":[],"createdAt":"2025-08-21 14:48:39","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7427321/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7427321/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":89650960,"identity":"a59538c3-668b-47e5-aa6a-bab12de5d26c","added_by":"auto","created_at":"2025-08-22 09:39:08","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":461431,"visible":true,"origin":"","legend":"","description":"","filename":"QDS.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7427321/v1_covered_678f90ab-600c-4b4e-8701-e5f725c8abb6.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eOne dimensional Quantum Droplets under the effect of curved space-time\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Kasdi Merbah Ouargla ","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Quantum droplets, Ultra cold atoms, Space-time curvature, Minimal momentum, Maximal length, Modified Heisenberg uncertainty principle","lastPublishedDoi":"10.21203/rs.3.rs-7427321/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7427321/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we study quantum droplets in one dimension under the influence of space-time curvature by \u0026nbsp;redefining the momentum operator ˆ P = −i(1 +αx^2)∂/∂x, resulting in a maximum length and a minimum \u0026nbsp;momentum, consistent with anti-de Sitter space (AdS). By analyzing this effect through the α parameter \u0026nbsp;on the exact solution of free quantum droplets, we find that the relationship between the number of atoms \u0026nbsp;and the chemical potential deviates from the ordinary case. Additionally, we observe that the characteristic \u0026nbsp;f \u0026nbsp;lat-top shape of quantum droplets can disappear, transforming into a Gaussian profile in the presence of the \u0026nbsp;maximum length (minimum momentum). Furthermore, our findings reveal that the interaction of quantum \u0026nbsp;droplets with space-time curvature results in an increase in their size. Finally, by studying this effect on the \u0026nbsp;variational solution using a Gaussian ansatz for small droplets, we conclude that α reduces the stability and \u0026nbsp;self-localization of the quantum droplets.\u003c/p\u003e","manuscriptTitle":"One dimensional Quantum Droplets under the effect of curved space-time","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-22 09:38:44","doi":"10.21203/rs.3.rs-7427321/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c571da47-e432-4577-92fe-722ae7333445","owner":[],"postedDate":"August 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-22T09:38:44+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-22 09:38:44","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7427321","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7427321","identity":"rs-7427321","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}