Master equations describing open quantum dynamics are typically first-order differential equations. When such dynamics brings the trajectories in state space of more than one initial state to the same point at finite instants in time, the generator of the corresponding master equation becomes singular while the dynamical map becomes noninvertible. The first-order, time-local, homogeneous master equations then fail to describe the dynamics beyond the singular point. Retaining time locality in the master equation necessitates a reformulation in terms of higher-order differential equations. We formulate a method to eliminate the divergent behavior of the generator by using a combination of higher-order derivatives of the generator with suitable weights and illustrate it with several examples. We also present a detailed study of the central spin model and we propose the average rate of information inflow in non-Markovian processes as a quantity that captures a different aspect of non-Markovian dynamics.

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具有奇点的开放量子动力学：主方程和非马尔可夫度

描述开放量子动力学的主方程通常是一阶微分方程。当这种动力学将多个初始状态的状态空间中的轨迹在有限时刻带到同一点时，相应主方程的生成器变得奇异，而动力学映射变得不可逆。一阶、时域、齐次主方程无法描述奇异点以外的动力学。在主方程中保留时间局部性需要根据高阶微分方程重新表述。我们通过使用具有合适权重的生成器的高阶导数的组合，制定了一种消除生成器发散行为的方法，并通过几个示例对其进行了说明。