Inequivalence of Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics for a single quantum spin

Quantum Physics [Submitted on 10 Apr 2026] Inequivalence of Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics for a single quantum spin Yuefei Liu, Olle Eriksson, Erik Sjöqvist 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 Journal reference: Phys. Rev. B 113, 134305 (2026) Related DOI: https://doi.org/10.1103/kf72-283n Focus to learn more Submission history From: Erik Sjoqvist [view email] [v1] Fri, 10 Apr 2026 20:53:29 UTC (1,687 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)