Erlangen 2026 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 5: Quantum Mechanics: Spectral Theory and Many-Body Systems
MP 5.4: Vortrag
Mittwoch, 18. März 2026, 14:45–15:00, KH 02.013
Beyond the rotating-wave approximation: error bounds for higher order approximations — •Leonhard Richter1, Robin Hillier2, Davide Lonigro1, and Daniel Burgarth1 — 1Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany — 2Department of Mathematics and Statistics, Lancaster University, UK
The rotating-wave approximation (RWA) is a widely used method for simplifying differential equations such as the Schrödinger equation in light-matter systems. However, its limitations have become more apparent with recent technological advancements highlighting the need for more sophisticated approximation schemes. Our aim is to address one particular drawback of the RWA: the error it introduces accumulates over time eventually rendering its application unjustified. In the case of bounded time-periodic Hamiltonians, the RWA is known to be the first order in the Floquet-Magnus expansion. Recently, a novel perspective on this expansion allowed to provide explicit error bounds that capture the time-dependence of each order reasonably well.
We extend this perspective to the unbounded case where the Floquet-Magnus expansion is generally not known to converge. Our approach iteratively constructs effective Hamiltonians that are time-independent in the interaction picture and scale with a specified order in frequency. Crucially, we are also able to provide explicit error bounds for the difference between the effective and original dynamics.
This work is in collaboration with Robin Hillier, Davide Lonigro, and Daniel Burgarth.
Keywords: rotating-wave approximation; Bloch-Siegert Hamiltonian; Floquet-Magnus; error bounds