Quantum Averaging Theory for Multi-Timescale Driven Quantum Systems

Kristian D. Barajas; Wesley C. Campbell

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arXiv · 2503.09761

Quantum Averaging Theory for Multi-Timescale Driven Quantum Systems

Kristian D. Barajas·Wesley C. Campbell

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Abstract

We present a multi-timescale Quantum Averaging Theory (QAT), a unitarity-preserving generalized Floquet framework for analytically modeling periodically and almost-periodically driven quantum systems across multiple timescales. By integrating the Magnus expansion with the method of averaging on multiple scales, QAT captures the effects of both far-detuned and near-resonant interactions on system dynamics. The framework yields an effective Hamiltonian description while retaining fast oscillatory effects within a separate dynamical phase operator, ensuring accuracy across a wide range of driving regimes. We demonstrate the rapid convergence of QAT results toward exact numerical solutions in both detuning regimes for touchstone problems in quantum information science.

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BibTeX RIS

Kristian D. Barajas, Wesley C. Campbell. 2025-12-31. Quantum Averaging Theory for Multi-Timescale Driven Quantum Systems. https://arxiv.org/abs/2503.09761

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