Multi-Timescale Quantum Averaging Theory for Driven Quantum Systems

• URL: http://arxiv.org/abs/2503.09761v1
• Date: Wed, 12 Mar 2025 19:00:24 GMT
• Title: Multi-Timescale Quantum Averaging Theory for Driven Quantum Systems
• Authors: Kristian D. Barajas, Wesley C. Campbell,
• Abstract summary: We present a multi-timescale Quantum Averaging Theory (QAT) for modeling periodically and almost-periodically driven quantum systems.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We present a multi-timescale Quantum Averaging Theory (QAT), a generalized unitarity-preserving analytic framework for 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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