The Dunkl-Fokker-Planck Equation in 1+1 Dimensions

The Dunkl-Fokker-Planck Equation in 1+1 Dimensions | 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 The Dunkl-Fokker-Planck Equation in 1+1 Dimensions Roberto Daniel Mota Esteves, Didier Ojeda Guillén, Miguel Alejandro Xicoténcatl Merino This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3871631/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Mar, 2024 Read the published version in Few-Body Systems → Version 1 posted 4 You are reading this latest preprint version Abstract By replacing the spatial derivative with the Dunkl derivative, we generalize the Fokker-Planck equation in (1+1) dimensions. We obtain the Dunkl-Fokker-Planck eigenvalues equation and solve it for the harmonic oscillator plus a centrifugal-type potential. Furthermore, when the drift function is odd, we reduce our results to those of the recently developed Wigner-Dunkl supersymmetry. PACS: 02.30.Ik, 02.30.Jr, 03.65.Ge, 05.10.Gg Dunkl derivative Fokker-Planck equation generalized harmonic oscillator Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 14 Mar, 2024 Read the published version in Few-Body Systems → Version 1 posted Editorial decision: Revision requested 19 Jan, 2024 Editor assigned by journal 17 Jan, 2024 Submission checks completed at journal 17 Jan, 2024 First submitted to journal 16 Jan, 2024 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. 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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-3871631","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":267745557,"identity":"8bde8ac4-fbd3-49ba-8f15-2febacd6d16e","order_by":0,"name":"Roberto Daniel Mota Esteves","email":"","orcid":"","institution":"Instituto Politécnico Nacional","correspondingAuthor":false,"prefix":"","firstName":"Roberto","middleName":"Daniel Mota","lastName":"Esteves","suffix":""},{"id":267745558,"identity":"d57cfbdd-fe9b-4ff2-9dad-470b09f7ef22","order_by":1,"name":"Didier Ojeda Guillén","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIie2RMQuCQBTHXxycyzPXi6TPIAgSNPRVmmw5h5ZawtG2nPsWTc6CZIs0hrvg0BQITRE9bVfbgu433PsP7wf3vwNQKH6RGIDRQBoUQZjfKHxRK9hbqS0LPm4Hw/PuWqwC3zTCrLrl2ymClpyObcooyzb2IUhQ5F40kyldDF03b1OsXLpjPYjREnpkS06KQKeP4qNlZKUtX72UZUoKo+6SFV7QQ6Eumo2XuovrMG8vkHd1oRcrC1z7cyNMiko+/ImhJWmrQh/hwIA3iYvmbF+v0UqAZ5PYvXtboVAo/pE3F7NF6kLlfVcAAAAASUVORK5CYII=","orcid":"","institution":"Instituto Politécnico Nacional","correspondingAuthor":true,"prefix":"","firstName":"Didier","middleName":"Ojeda","lastName":"Guillén","suffix":""},{"id":267745559,"identity":"05c598cd-c75b-4019-ac7c-cb3d90d6e998","order_by":2,"name":"Miguel Alejandro Xicoténcatl Merino","email":"","orcid":"","institution":"Center for Research and Advanced Studies of the National Polytechnic Institute","correspondingAuthor":false,"prefix":"","firstName":"Miguel","middleName":"Alejandro Xicoténcatl","lastName":"Merino","suffix":""}],"badges":[],"createdAt":"2024-01-17 02:45:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3871631/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3871631/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00601-024-01898-1","type":"published","date":"2024-03-14T15:00:42+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":52907255,"identity":"1e628f90-821d-427e-84a8-a07de9c04f6b","added_by":"auto","created_at":"2024-03-18 15:11:30","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":199008,"visible":true,"origin":"","legend":"","description":"","filename":"DunklFokkerPlanckFBS.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3871631/v1_covered_12838af7-7e3e-432b-8359-565eb3e54aeb.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eThe Dunkl-Fokker-Planck Equation in 1+1 Dimensions\u003c/p\u003e","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":"Dunkl derivative, Fokker-Planck equation, generalized harmonic oscillator","lastPublishedDoi":"10.21203/rs.3.rs-3871631/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3871631/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBy replacing the spatial derivative with the Dunkl derivative, we generalize the Fokker-Planck equation in (1+1) dimensions. 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