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arXiv · 2504.20533

Error bounds for the Floquet-Magnus expansion and their application to the semiclassical quantum Rabi model

Anirban Dey·Davide Lonigro·Kazuya Yuasa·Daniel Burgarth
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Abstract

We present a general, nonperturbative method for deriving effective Hamiltonians of arbitrary order for periodically driven systems, based on an iterated integration by parts technique. The resulting family of effective Hamiltonians reproduces the well-known Floquet-Magnus expansion, now enhanced with explicit error bounds that quantify the distance between the exact and approximate dynamics at each order, even in cases where the Floquet-Magnus series fails to converge. We apply the method to the semiclassical Rabi model and provide explicit error bounds for both the Bloch-Siegert Hamiltonian and its third-order refinement. Our analysis shows that, while the rotating-wave approximation more accurately captures the true dynamics than the Bloch-Siegert Hamiltonian in most regimes, the third-order approximation ultimately outperforms both.

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Anirban Dey, Davide Lonigro, Kazuya Yuasa, Daniel Burgarth. 2025-04-29. Error bounds for the Floquet-Magnus expansion and their application to the semiclassical quantum Rabi model. https://doi.org/10.1103/6bgj-s987

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