Defining a quantum active particle using a non-unitary quantum walk

Defining a quantum active particle using a non-unitary quantum walk | 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 Article Defining a quantum active particle using a non-unitary quantum walk Manami Yamagishi, Naomichi Hatano, Hideaki Obuse This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4796209/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 Nov, 2024 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract The main aim of the present paper is to define an active particle in a quantum framework as a minimal model of quantum active matter and investigate difference and commonalities of quantum and classical active matters. Although the research field of active matter has been expanding wider and wider, most research is conducted in classical systems. We here propose a truly deterministic quantum active-particle model with a non-unitary quantum walk as minimal models of quantum active matter. We aim to reproduce similar results obtained previously with classical active Brownian particle; that is, a Brownian particle, with a finite energy take-up, becomes active and climbs up a potential wall. We realize such a system with non-unitary quantum walks. We introduce new internal states, the ground state |G⟩ and the excited state |E⟩, and a new non-unitary operator N(g) for an asymmetric transition between |G⟩ and |E⟩. The non-Hermiticity parameter g promotes transition to the excited state and hence the particle takes up energy from the environment. With our quantum active particle, we successfully observe that the movement of the quantum walker becomes more active in a non-trivial way as we increase the non-Hermiticity parameter g, which is similar to the classical active Brownian particle. Meanwhile, we also observe three unique features of quantum walks, namely, ballistic propagation of peaks in one dimension, the walker staying on the constant energy plane in two dimensions, and oscillations originating from the resonant transition between the ground state |G⟩ and excited state |E⟩ both in one and two dimensions. Physical sciences/Physics/Quantum physics/Theoretical physics Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Statistical physics Full Text Additional Declarations No competing interests reported. Supplementary Files yamagishiqABPpapersuppl20240719.pdf Cite Share Download PDF Status: Published Journal Publication published 19 Nov, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 28 Aug, 2024 Reviews received at journal 22 Aug, 2024 Reviews received at journal 21 Aug, 2024 Reviewers agreed at journal 12 Aug, 2024 Reviewers agreed at journal 11 Aug, 2024 Reviewers invited by journal 09 Aug, 2024 Editor assigned by journal 09 Aug, 2024 Editor invited by journal 06 Aug, 2024 Submission checks completed at journal 02 Aug, 2024 First submitted to journal 24 Jul, 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. 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-4796209","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":343670942,"identity":"21065df4-bd6e-4a41-b5f7-bdb7d10b3624","order_by":0,"name":"Manami Yamagishi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+klEQVRIiWNgGAWjYNACAxseNhgTSrPhUgtTlwbVkkC0FobDUBqhBTfQbT978NONgvMyfPwH2CQYf9gYGxxvYPzwg4EvD5cWszN5ydI5Brd52CQS2CQYEtLMDM4cYJbsYWArxqnlQI4BVAsDm/SfhMM2BjcSGKSBfklswKXl/Bvj3zkG53jYQA5jgGhh/o1Xy40cM6AtB4AhBnbYYTOgFjb8ttx4Y2adY5AMdFhiswVDWpqx5JmDbZY9Bnj8cj7H+HbOHzt7+f7DB28w2NgY9h1vPnzjR8UxnCGGBBghLlE4AGIYHEsgQgsUyEN01pCgZRSMglEwCoY5AACjZUzkiyoO0gAAAABJRU5ErkJggg==","orcid":"","institution":"The University of Tokyo","correspondingAuthor":true,"prefix":"","firstName":"Manami","middleName":"","lastName":"Yamagishi","suffix":""},{"id":343670943,"identity":"7cf9344f-d84d-45d4-a25f-259b224f8386","order_by":1,"name":"Naomichi Hatano","email":"","orcid":"","institution":"The University of Tokyo","correspondingAuthor":false,"prefix":"","firstName":"Naomichi","middleName":"","lastName":"Hatano","suffix":""},{"id":343670944,"identity":"be12b5b2-232c-46b1-8a1e-17104aa06f98","order_by":2,"name":"Hideaki Obuse","email":"","orcid":"","institution":"Hokkaido University","correspondingAuthor":false,"prefix":"","firstName":"Hideaki","middleName":"","lastName":"Obuse","suffix":""}],"badges":[],"createdAt":"2024-07-24 14:39:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4796209/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4796209/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-78986-z","type":"published","date":"2024-11-19T15:57:36+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":69835173,"identity":"2c69bcaa-b8bf-4a82-aa8c-9201d54067ee","added_by":"auto","created_at":"2024-11-25 16:12:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1847709,"visible":true,"origin":"","legend":"","description":"","filename":"20240802forsubmission.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4796209/v1_covered_a1b9f55d-d621-4965-8774-6a6bb9f511a2.pdf"},{"id":63145626,"identity":"b68301c2-c628-4c31-93eb-cf34c8e04644","added_by":"auto","created_at":"2024-08-23 16:32:37","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1181862,"visible":true,"origin":"","legend":"","description":"","filename":"yamagishiqABPpapersuppl20240719.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4796209/v1/bcd0975527847ba929fc2718.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Defining a quantum active particle using a non-unitary quantum walk","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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4796209/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4796209/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The main aim of the present paper is to define an active particle in a quantum framework as a minimal model of quantum active matter and investigate difference and commonalities of quantum and classical active matters. 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