Generalized Aharonov-Bohm Effect

Quantum Physics arXiv:2601.17659 (quant-ph) [Submitted on 25 Jan 2026] Title:Generalized Aharonov-Bohm Effect Authors:Shan Gao View a PDF of the paper titled Generalized Aharonov-Bohm Effect, by Shan Gao View PDF HTML (experimental) Abstract:The Aharonov-Bohm (AB) effect highlights the fundamental role of electromagnetic potentials in quantum mechanics, manifesting as a phase shift for a charged particle in field-free regions. While well-established for static magnetic fluxes, the effect's behavior under time-varying fluxes remains an open and debated question. Employing the WKB method, we derive the AB phase shift for a time-dependent magnetic vector potential, demonstrating that for circular paths in the quasistatic regime, it is proportional to the time-averaged enclosed magnetic flux, \(\Delta \phi_{\rm AB} = \frac{1}{T} \int_0^T e \Phi(t) \, dt\), with the total phase shift, including kinetic contributions, equaling \(e \Phi(0)\). For non-circular paths, the phase shift depends on both the flux history and path geometry, revealing the effect's hybrid nature involving gauge potentials and induced electric fields. We verify the consistency of our gauge choice with Maxwell's equations and discuss the implications for local versus nonlocal interpretations of the AB effect. We also generalize the results to scenarios with nonzero external magnetic fields, where the enclosed flux is through the actual electron paths, and for circular paths of radius $R$, the AB phase shift is also proportional to the time average of the enclosed flux \(\Phi_{\rm enc}(R,t)\), with the total phase shift depending only on the initial enclosed flux \(e \Phi_{\rm enc}(R,0)\); for general non-circular paths, the external magnetic field affects trajectories and phase accumulation through the Lorentz force, leading to additional path dependence. These findings clarify the role of gauge-dependent potentials and induced fields in the generalized AB effect, offering new theoretical insights and potential applications in quantum technologies. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.17659 [quant-ph] (or arXiv:2601.17659v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.17659 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Journal reference: Found Phys 55, 85 (2025) Related DOI: https://doi.org/10.1007/s10701-025-00900-y Focus to learn more DOI(s) linking to related resources Submission history From: Shan Gao [view email] [v1] Sun, 25 Jan 2026 02:35:26 UTC (12 KB) Full-text links: Access Paper: View a PDF of the paper titled Generalized Aharonov-Bohm Effect, by Shan GaoView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)