Higher order Magnus expansions for two-level quantum dynamics

Quantum Physics [Submitted on 14 Mar 2026] Higher order Magnus expansions for two-level quantum dynamics Chen Wei, Frank Großmann We investigate the Magnus expansion for a generic time-dependent two-level system under single-axis driving. By virtue of the \(\mathfrak{su}(2)\) Lie algebra, the expansion is decomposed into a commutator-free form. To illustrate the usefulness of the gained expression, we then revisit the Landau-Zener-Stückelberg-Majorana model, with a focus on non-adiabatic transitions as well as the Stokes phase. In addition, the semiclassical Rabi model is systematically treated by determining the Floquet quasienergy up to different orders. We demonstrate how to employ suitable picture transformations as well as on how to enforce the symmetry of the underlying model in order to guarantee convergence of the expansion as well as to achieve satisfactory agreement with the exact results. For both models that we studied it turns out that a third order approximation yields results that are in next to perfect agreement with exact analytical ones. Surprisingly, in the case of the semiclassical Rabi model, even the second order Magnus approximation in the adiabatic picture produces almost exact results over the whole parameter range. Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2603.13821 [quant-ph]   (or arXiv:2603.13821v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.13821 Focus to learn more Submission history From: Chen Wei [view email] [v1] Sat, 14 Mar 2026 08:12:04 UTC (102 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: math math-ph math.MP 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?)