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

Dey A, Lonigro D, Yuasa K, Burgarth D (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Physical Review A American Physical Society

Book Volume: 112

Article Number: 053723

DOI: 10.1103/6bgj-s987

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.

Authors with CRIS profile

Davide Lonigro Professur für Theoretische Physik Daniel Burgarth Professur für Theoretische Physik

Involved external institutions

Waseda University / 早稲田大学 JP Japan (JP) Macquarie University AU Australia (AU)

How to cite

APA:

Dey, A., Lonigro, D., Yuasa, K., & Burgarth, D. (2025). Error bounds for the Floquet-Magnus expansion and their application to the semiclassical quantum Rabi model. Physical Review A, 112. https://doi.org/10.1103/6bgj-s987

MLA:

Dey, Anirban, et al. "Error bounds for the Floquet-Magnus expansion and their application to the semiclassical quantum Rabi model." Physical Review A 112 (2025).

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