The Floquet-Magnus expansion of unbounded operators

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.

Mathematical Physics (math-ph); Functional Analysis (math.FA); Quantum Physics (quant-ph)

arXiv:2605.23734 [math-ph]

(or arXiv:2605.23734v2 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2605.23734 Focus to learn more arXiv-issued DOI via DataCite

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