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arXiv · 2605.23734

The Floquet-Magnus expansion of unbounded operators

Daniel Burgarth·Robin Hillier·Davide Lonigro·Leonhard Richter
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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.

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Daniel Burgarth, Robin Hillier, Davide Lonigro, Leonhard Richter. 2026-05-22. The Floquet-Magnus expansion of unbounded operators. https://arxiv.org/abs/2605.23734

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