Abstract:The Floquet-Magnus expansion is a widely used tool to derive effective descriptions of time-periodic quantum systems by approximating their dynamics with a time-independent Hamiltonian. However, its standard formulation is, strictly speaking, restricted to bounded Hamiltonians. In this work, we extend its definition and analysis to a broad class of time-periodic unbounded Hamiltonians. Our approach is based on an a priori distinct nonperturbative framework for the construction of effective Hamiltonians, which we show to reproduce the Floquet-Magnus expansion. A particular strength of our framework is that it allows us to prove that the resulting effective dynamics approximates the original time evolution propagators to arbitrary order in the high-frequency limit without requiring convergence of the Floquet-Magnus expansion, a condition that is already highly restrictive even in the bounded setting. We illustrate the scope of the method on representative models: the quantum Rabi Hamiltonian in the interaction picture, and the periodically driven quantum harmonic oscillator.
| Comments: | 62 pages |
| Subjects: | Mathematical Physics (math-ph); Functional Analysis (math.FA); Quantum Physics (quant-ph) |
| MSC classes: | 46N50, 47N50, 47A58, 81Q10 |
| Cite as: | arXiv:2605.23734 [math-ph] |
| (or arXiv:2605.23734v1 [math-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2605.23734 arXiv-issued DOI via DataCite (pending registration) |
From: Leonhard Richter [view email]
[v1]
Fri, 22 May 2026 15:11:17 UTC (69 KB)
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