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arXiv:1802.08897 · The European Physical Journal D

Applications of Picard and Magnus expansions to the Rabi model

Fabrizio Angaroni, Giuliano Benenti, G. Strini

Published Oct 1, 2018• 10 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2018-90190-y

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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.