Inequivalence of Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics for a single quantum spin
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Quantum Physics arXiv:2604.09900 (quant-ph) [Submitted on 10 Apr 2026] Title:Inequivalence of Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics for a single quantum spin Authors:Yuefei Liu, Olle Eriksson, Erik Sjöqvist View a PDF of the paper titled Inequivalence of Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics for a single quantum spin, by Yuefei Liu and 2 other authors View PDF HTML (experimental) Abstract:We examine the relation between the quantum Landau-Lifshitz equation ($q$-LL) [Phys. Rev. Lett. 110, 147201 (2013)] and quantum Landau-Lifshitz-Gilbert equation ($q$-LLG) [Phys. Rev. Lett. 133, 266704 (2024)]; two non-linear purity preserving master equations that extend classical atomistic spin dynamics into the quantum regime. While the classical LL and LLG counterparts for any number of spins are known to be equivalent, i.e., give identical spin trajectories up to a rescaling of the time parameter, the quantum formulations are equivalent only in certain cases, such as for pure states or for arbitrary single spin-$\frac{1}{2}$ states. Here, we demonstrate that this equivalence breaks down even at the level of a single spin, provided $s \geq 1$. Focusing on a spin-1 particle in an anisotropic crystal field, we show that the $q$-LL and $q$-LLG equations generate inequivalent time evolution. We introduce temporal rescaling misfits that quantify the inequivalence of the two types of dynamics. Although our results highlight fundamental differences in dissipation mechanisms encoded in these equations, the resulting trajectories remain qualitatively similar for this system. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.09900 [quant-ph] (or arXiv:2604.09900v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.09900 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Journal reference: Phys. Rev. B 113, 134305 (2026) Related DOI: https://doi.org/10.1103/kf72-283n Focus to learn more DOI(s) linking to related resources Submission history From: Erik Sjoqvist [view email] [v1] Fri, 10 Apr 2026 20:53:29 UTC (1,687 KB) Full-text links: Access Paper: View a PDF of the paper titled Inequivalence of Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics for a single quantum spin, by Yuefei Liu and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?) 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?)