Random Walks Through Fock States of a Graph

Random Walks Through Fock States of a Graph | 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Download PDF Research Article Random Walks Through Fock States of a Graph Manfred Harringer This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3372215/v6 This work is licensed under a CC BY 4.0 License Status: Posted Version 6 posted You are reading this latest preprint version Show more versions Abstract I present process models for motion on a graph Γ(V,E) along its edges, motivated by examples. I build random sequences of edges and I derive sequences of Fock states. Therefore, I can distinguish two kinds of process steps, acceptance and rejection, comparable to stimulated and spontaneous emission. There is always at least one vertex, which represents the vacuum of the system. Rejections and vacuum are not visible in a quantum grand canonical ensemble. Random walk Markov chain Fock states forward and backward motion harmonic oscillator vacuum Full Text Additional Declarations The authors declare no competing interests. Supplementary Files XXDATA.xlsx Cite Share Download PDF Status: Posted Version 6 posted You are reading this latest preprint version Show more versions 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-3372215","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":266107043,"identity":"a5cced70-a405-46a1-b0d5-134ccf863a8a","order_by":0,"name":"Manfred Harringer","email":"data:image/png;base64,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","orcid":"","institution":"Herr | Mister","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Manfred","middleName":"","lastName":"Harringer","suffix":""}],"badges":[],"createdAt":"2023-09-20 09:33:03","currentVersionCode":6,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false,"coiExplicitlySet":false},"doi":"10.21203/rs.3.rs-3372215/v6","doiUrl":"https://doi.org/10.21203/rs.3.rs-3372215/v6","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":54111887,"identity":"0fe88498-cedf-48ba-b4cf-d8d8b27ebe09","added_by":"auto","created_at":"2024-04-04 18:32:26","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":389852,"visible":true,"origin":"","legend":"","description":"","filename":"RandomWalksThroughFockStatesofaGraph.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3372215/v6_covered_6f9af52b-e4ae-44a3-bd66-ebf0acb2506e.pdf"},{"id":54111015,"identity":"18e344df-7a9a-4043-9541-ea2f1922729a","added_by":"auto","created_at":"2024-04-04 18:16:23","extension":"xlsx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":32723,"visible":true,"origin":"","legend":"","description":"","filename":"XXDATA.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-3372215/v6/d32c56b05e1e176765c2219d.xlsx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eRandom Walks Through Fock States of a Graph\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Random walk, Markov chain, Fock states, forward and backward motion, harmonic oscillator, vacuum","lastPublishedDoi":"10.21203/rs.3.rs-3372215/v6","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3372215/v6","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eI present process models for motion on a graph Γ(V,E) along its edges, motivated by examples. 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