For studying quantum phenomena in time, it is vital to have a profound understanding of the classical dynamics. For this reason, we derive equations of motions describing the classical propagation of a quantum system. A comparison of this classical evolution with the actual temporal behavior enables us to identify quantum effects of the evolution itself and distinguish them from static quantum features and quantum phenomena for a single point in time. As applications of our universal technique, we analyze nonlinear processes in quantum optics, semi-classical models, and the multipartite entanglement dynamics of macroscopic ensembles.

中文翻译：

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量子系统中的经典演化

为了及时研究量子现象，对经典动力学有深刻的理解至关重要。因此，我们推导出描述量子系统经典传播的运动方程。这种经典演化与实际时间行为的比较使我们能够识别演化本身的量子效应，并将它们与单个时间点的静态量子特征和量子现象区分开来。作为我们通用技术的应用，我们分析了量子光学、半经典模型和宏观系综的多分纠缠动力学中的非线性过程。