Landau levels in a time-dependent magnetic field: the Madelung fluid perspective

[2505.08460] Landau levels in a time-dependent magnetic field: the Madelung fluid perspective Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2505.08460 (quant-ph) [Submitted on 13 May 2025 ( v1 ), last revised 4 Jul 2026 (this version, v3)] Title: Landau levels in a time-dependent magnetic field: the Madelung fluid perspective Authors: Nicolas Perez , Eyal Heifetz View a PDF of the paper titled Landau levels in a time-dependent magnetic field: the Madelung fluid perspective, by Nicolas Perez and Eyal Heifetz View PDF HTML (experimental) Abstract: We revisit the quantum dynamics of a charged particle in a time-dependent magnetic field, a fundamental problem exhibiting rich non-adiabatic behaviour, from the complementary perspective of the Madelung fluid formulation. We first analyse the system within standard quantum mechanics using perturbation theory around the Landau levels, and then address the same problem through the Madelung perspective. We show that the hydrodynamic formulation not only yields an intuitive derivation of the exact solution, it also provides a clear physical interpretation of non-adiabatic quantum evolution in terms of mechanical energy transfers. In this picture, the sloshing oscillations of the wave function arise from deviations from the force balance between the magnetic Lorentz force and the gradient of the Bohm potential within the Landau levels. More broadly, our study illustrates how the Madelung approach reveals unexpected analogies between quantum dynamics and phenomena familiar from geophysical fluid dynamics. Comments: 21 pages, 6 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2505.08460 [quant-ph] (or arXiv:2505.08460v3 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2505.08460 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Nicolas Perez [ view email ] [v1] Tue, 13 May 2025 11:41:24 UTC (4,964 KB) [v2] Tue, 14 Apr 2026 01:44:45 UTC (5,720 KB) [v3] Sat, 4 Jul 2026 11:44:10 UTC (5,625 KB) Full-text links: Access Paper: View a PDF of the paper titled Landau levels in a time-dependent magnetic field: the Madelung fluid perspective, by Nicolas Perez and Eyal Heifetz View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2025-05 References & Citations INSPIRE HEP NASA ADS Google 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? ) 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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