We derive a Markovian master equation that models the evolution of systems subject to driving and control fields. Our approach combines time rescaling and weak-coupling limits for the system-environment interaction with a secular approximation. The derivation makes use of the adiabatic time-evolution operator in a manner that allows for the efficient description of strong driving, while recovering the well-known adiabatic master equation in the appropriate limit. To illustrate the effectiveness of our approach, firstly we apply it to the paradigmatic case of a two-level (qubit) system subject to a form of periodic driving that remains unsolvable using a Floquet representation and lastly we extend this scenario to the situation of two interacting qubits, the first driven while the second one directly in contact with the environment. We demonstrate the reliability and broad scope of our approach by benchmarking the solutions of the derived reduced time evolution against numerically exact simulations using tensor networks. Our results provide rigorous conditions that must be satisfied by phenomenological master equations for driven systems that do not rely on first-principles derivations.

中文翻译：

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超出绝热极限的时间相关马尔可夫主方程


我们推导出一个马尔可夫主方程，该方程模拟受驱动和控制场影响的系统演变。我们的方法将系统-环境交互的时间重新缩放和弱耦合极限与长期近似相结合。该推导利用绝热时间演化算子，以允许有效描述强驱动，同时在适当的限制内恢复众所周知的绝热主方程。为了说明我们方法的有效性，首先，我们将其应用于两级（量子比特）系统的范例，该系统受到一种周期性驱动形式的影响，该驱动形式仍然无法使用 Floquet 表示来解决，最后，我们将此场景扩展到两个交互量子比特的情况，第一个量子比特被驱动，而第二个量子比特直接与环境接触。我们通过使用张量网络将推导出的减少时间演变的解决方案与数值精确模拟进行基准测试，证明了我们方法的可靠性和广泛范围。我们的结果提供了严格的条件，对于不依赖于第一性原理推导的驱动系统，现象学主方程必须满足这些条件。