Second-neighbor hopping effects on the dynamics of breathers in 2D quantum ultracold atoms loaded in optical lattices

Second-neighbor hopping effects on the dynamics of breathers in 2D quantum ultracold atoms loaded in optical lattices | 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 Second-neighbor hopping effects on the dynamics of breathers in 2D quantum ultracold atoms loaded in optical lattices Zacharie Isidore Djoufack, Jean Pierre Nguenang, Aurélin Kenfack-Jiotsa This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5321036/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 We explore analytically and numerically the dual role played bythe second-neighbor hopping on the modulation instability and onthe dynamics of breathers in 2D quantum ultracold atoms loaded inoptical lattices. Via the linear stability analysis, it is shownthat the dispersion relation formed exhibits intriguing forms. Itis found that, the existence conditions of appearance of themodulational intability (MI) regions and the growth rate may besignificantly affected by the second neighbor hopping couplingstrength. To support the analytical studies, direct numericalsimulations of MI is carried out to show the generation of a trainof short waves exhibiting periodic W-shaped and V-shaped solitonswith decreasing amplitude as time evolves. The emergence ofbreathers in the regions where the MI manifests is predicted to beinfluenced by the second neighbor hopping coupling strength. Bymaking use of Rayleigh-Ritz variational method and in agreementwith the MI analysis, the analytical results reveal the existenceof the radial symmetric modes called the dynamics of breathers.The accuracy of the outcomes is checked by numerical calculationswhich show a good agreement with the theoretical analysis. Dynamics of breathers Modulational instability Optical lattice Quantum ultracold atoms Full Text Additional Declarations No competing interests reported. Supplementary Files Supplementaryfiles.rar 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-5321036","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":374461122,"identity":"c5b3c18f-a5d4-451a-97c7-e8f7fb2e3b8a","order_by":0,"name":"Zacharie Isidore Djoufack","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEUlEQVRIie2SsWrDMBCGrxQ0pXHHEw7NKzgYlAwmz+IiSBbPxUNIMyVLaFdvfYhCpg5nDJ78ABozafLgKVAopXKztLhy10L1gbifg0/SCQE4HH8RIoAUIDCRmYXgnUNbe5Tqq8I3Z8VUmwLfFJPoF2WYFyXSah6Od4U+vr7MbkIl9bFJAacWh1O5QCqluNgvppO9xlAoE7IKcEQ/KwFVwm8YRZeQMBwQ3h5ULPyrLazRcrFWQXqniHk142+E98/Z8tQq2KvkWxIDTJhvTokDTESvYmaRs/xBhoha+CNCM0Z9x7MKrcpQFbmi03zy9Cg1r2k99nbLAzZpZFUAO+9yHX/2bYL5F5tOp7OJw+Fw/HM+APm/XKUaVFrgAAAAAElFTkSuQmCC","orcid":"","institution":"University of Dschang","correspondingAuthor":true,"prefix":"","firstName":"Zacharie","middleName":"Isidore","lastName":"Djoufack","suffix":""},{"id":374461123,"identity":"d5ff7a10-e280-4a00-b684-1235e7a21a09","order_by":1,"name":"Jean Pierre Nguenang","email":"","orcid":"","institution":"University of Douala","correspondingAuthor":false,"prefix":"","firstName":"Jean","middleName":"Pierre","lastName":"Nguenang","suffix":""},{"id":374461124,"identity":"68ba4344-9628-4831-b63e-326637f099ef","order_by":2,"name":"Aurélin Kenfack-Jiotsa","email":"","orcid":"","institution":"University of Yaoundé I","correspondingAuthor":false,"prefix":"","firstName":"Aurélin","middleName":"","lastName":"Kenfack-Jiotsa","suffix":""}],"badges":[],"createdAt":"2024-10-23 18:53:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5321036/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5321036/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":68560255,"identity":"4cc5d1ef-1b75-456e-b489-f58625ed6571","added_by":"auto","created_at":"2024-11-08 14:09:03","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6202254,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5321036/v1_covered_13bc10ab-eb11-43c7-9490-17203432f4dc.pdf"},{"id":68319627,"identity":"ca020ed5-e1ae-4662-a752-e6dbb6590a9d","added_by":"auto","created_at":"2024-11-06 04:20:18","extension":"rar","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":12672580,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementaryfiles.rar","url":"https://assets-eu.researchsquare.com/files/rs-5321036/v1/6aa4919908aadf9e6e7e6578.rar"}],"financialInterests":"No competing interests reported.","formattedTitle":"Second-neighbor hopping effects on the dynamics of breathers in 2D quantum ultracold atoms loaded in optical lattices","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"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":"Dynamics of breathers , Modulational instability , Optical lattice , Quantum ultracold atoms","lastPublishedDoi":"10.21203/rs.3.rs-5321036/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5321036/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We explore analytically and numerically the dual role played bythe second-neighbor hopping on the modulation instability and onthe dynamics of breathers in 2D quantum ultracold atoms loaded inoptical lattices. 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