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 63.7: Poster

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

Floquet-Magnus expansion for driven quantum systems and spin dynamic mean-field theory in NMR — •Antonia Joëlle Bock — TU Dortmund University, Germany

An accurate and reliable theoretical description of periodically driven quantum systems is highly relevant to many applications, such as for magic-angle spinning (MAS) in nuclear magnetic resonance (NMR) and ultracold atoms in driven optical lattices. Typically, the first step in capturing the dynamics is to determine an effective time-independent Hamiltonian, for which one can choose from a broad range of slightly different, hence often confusing, theories. Thus, I specifically investigated two widely used theories: Average Hamiltonian theory (AHT) and the Floquet-van Vleck approach (secular averaging). I was able to quantify the importance of the kick operator for the equivalence between perturbative and numerically exact approaches. This was achieved through analytical calculations and numerical evaluations of exemplary spin systems. These crucial insights then build the foundation for the second step of my project: a dynamic mean-field theory for dense spin ensembles applicable to complex couplings between three or more spins (MAS-DMFT). The recently developed spinDMFT (cp., e.g., Gräßer et al., 2024) has proven to be efficient, accurate and applicable to large spin systems yielding 2-particle interactions.

Keywords: Floquet theory; Average Hamiltonian theory; Magnus expansion; nuclear magnetic resonance; magic-angle spinning