Error bounds for the Floquet-Magnus expansion and their application to the semiclassical quantum Rabi model
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909921091518464 |
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| author | Dey, Anirban Lonigro, Davide Yuasa, Kazuya Burgarth, Daniel |
| author_facet | Dey, Anirban Lonigro, Davide Yuasa, Kazuya Burgarth, Daniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20533 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Error bounds for the Floquet-Magnus expansion and their application to the semiclassical quantum Rabi model Dey, Anirban Lonigro, Davide Yuasa, Kazuya Burgarth, Daniel Quantum Physics 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. |
| title | Error bounds for the Floquet-Magnus expansion and their application to the semiclassical quantum Rabi model |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2504.20533 |