Dresden 2026 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 63: Quantum Dynamics and Many-body Systems – Poster (joint session DY/TT)

TT 63.10: Poster

Mittwoch, 11. März 2026, 15:00–18:00, P5

Higher order Magnus expansion for two-level quantum dynamics — •Chen Wei and Frank Großmann — Institut für Theoretische Physik, 01062 Dresden, Germany

This study investigates the Magnus expansion[1] for a generic time-dependent two-level system. By using its convergence condition[2], we find that elementary unitary transformations significantly extend the validity of the Magnus expansion. Furthermore, higher order terms admit particular physical interpretations. By virtue of su(2) Lie algebra, the expansion is decomposed into a commutator-free form. To illustrate its usefulness, we study the Landau-Zener[3] model, which displays a special case of non-adiabatic transitions. Using agian the Magnus expansion, Hermitian and non-Hermitian versions of the semiclassical Rabi model are systematically treated by determining the Floquet quasienergy[4] and Bloch-Siegert shift[5]. As a noteworthy by-product, the Magnus expansion provides a quantitative characterization of the adiabatic theorem[6].

[1] W. Magnus, Commun. Pure Appl. Math. 7, 649-673 (1954). [2] M. M. Maricq, J. Chem. Phys. 86, 5647-5651 (1987). [3] C. Zener and R. H. Fowler, Proc. R. Soc. Lond. A 137, 696-702 (1932). [4] J. H. Shirley, Phys. Rev. 138, B979 B987 (1965). [5] F. Bloch and A. Siegert, Phys. Rev. 57, 522-527 (1940). [6] M. Born and V. Fock, Z. Phys. 51, 165-180 (1928).

Keywords: Magnus expansion; two-level system; quantum dynamics; Landau-Zener transition; Floquet quasienergy