We introduce a dynamical picture, referred to as correlation picture, which connects a correlated bipartite state to its uncorrelated counterpart. This picture allows us to derive an exact dynamical equation for a general open-system dynamics with system-environment correlations included. This exact dynamics is in the form of a Lindblad-like equation even in the presence of initial system-environment correlations. For explicit calculations, we also develop a weak-correlation expansion that allows us to introduce systematic perturbative approximations. This expansion provides approximate master equations that can feature advantages over existing weak-coupling techniques. As a special case, we derive a Markovian master equation, which is different from existing approaches. We compare our equations with corresponding standard weak-coupling equations using two examples, for which our correlation-picture formalism is more accurate, or at least as accurate as the weak-coupling equations.

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开放式系统动力学的相关图法

我们介绍了一种动态图片，称为相关图片，该图片将相关的二分态连接到其不相关的对应物。这张图片使我们能够为包含系统环境相关性的一般开放系统动力学导出精确的动力学方程。即使在存在初始系统-环境相关性的情况下，这种精确的动力学也以类似于Lindblad方程的形式存在。对于显式计算，我们还开发了弱相关展开式，使我们可以引入系统的扰动逼近。这种扩展提供了近似主方程，该方程可以具有优于现有弱耦合技术的优点。作为一种特殊情况，我们推导了一个马尔可夫主方程，该方程不同于现有方法。