{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:37:22Z","timestamp":1760146642547,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T00:00:00Z","timestamp":1732665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Department of Science and Technology\u2014Science Education Institute (DOST-SEI) of the Philippine government","award":["MEMO-STSD-2023-654","UIDB\/MAT\/04674\/2020"],"award-info":[{"award-number":["MEMO-STSD-2023-654","UIDB\/MAT\/04674\/2020"]}]},{"DOI":"10.13039\/501100001871","name":"Center for Research in Mathematics and Applications (CIMA)","doi-asserted-by":"publisher","award":["MEMO-STSD-2023-654","UIDB\/MAT\/04674\/2020"],"award-info":[{"award-number":["MEMO-STSD-2023-654","UIDB\/MAT\/04674\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The Aharonov\u2013Bohm effect can be described as a phase difference in interfering charged particles that travel through two distinct pathways oppositely surrounding a perpendicularly-positioned solenoid. The magnetic field emanates from the solenoid but does not intersect the pathways. On the other hand, the Kuramoto model can be used to identify the synchronization conditions that lead to a particular phase difference by treating the phases as coupled oscillators. Starting with the overall wave function expression for the electron in an Aharonov\u2013Bohm potential, we derive a version of the Kuramoto model describing the phase dynamics of the bound state of the quantum mechanical system. We show that the resulting synchronization condition of the model coincides with the allowable values of the flux parameter for our case to achieve an Aharonov\u2013Bohm effect.<\/jats:p>","DOI":"10.3390\/axioms13120828","type":"journal-article","created":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T10:05:56Z","timestamp":1732701956000},"page":"828","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Kuramoto Model for the Bound State Aharonov\u2013Bohm Effect"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5583-8714","authenticated-orcid":false,"given":"Alviu Rey","family":"Nasir","sequence":"first","affiliation":[{"name":"Department of Physics, College of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, Iligan City 9200, Philippines"},{"name":"Premier Research Institute of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, Iligan City 9200, Philippines"},{"name":"Department of General Education, Initao College, Initao 9022, Philippines"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5207-1703","authenticated-orcid":false,"given":"Jos\u00e9 Lu\u00eds","family":"Da Silva","sequence":"additional","affiliation":[{"name":"CIMA Faculdade de C\u00eancias Exatas e da Engenharia, Campus Universit\u00e1rio da Penteada, Universidade da Madeira, 9020-105 Funchal, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0633-1583","authenticated-orcid":false,"given":"Jingle","family":"Magallanes","sequence":"additional","affiliation":[{"name":"Department of Physics, College of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, Iligan City 9200, Philippines"},{"name":"Premier Research Institute of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, Iligan City 9200, Philippines"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4142-0939","authenticated-orcid":false,"given":"Herry Pribawanto","family":"Suryawan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Technology, Sanata Dharma University, Yogyakarta 55283, Indonesia"}]},{"given":"Roshin Marielle","family":"Nasir-Britos","sequence":"additional","affiliation":[{"name":"Department of Physics, College of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, Iligan City 9200, Philippines"},{"name":"Premier Research Institute of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, Iligan City 9200, Philippines"},{"name":"Department of General Education, Initao College, Initao 9022, Philippines"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1103\/PhysRev.115.485","article-title":"Significance of electromagnetic potentials in the quantum theory","volume":"115","author":"Aharonov","year":"1959","journal-title":"Phys. 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