Abstract

Following the ideas N. N. Bogoliubov used to derive the classical and quantum nonlinear kinetic equations, we derive the Redfield quantum linear master equation, which is widely used in the theory of open quantum systems. This method allows one to calculate the joint state of a system and a reservoir at every instant of time, as well as to obtain quantum master equations as autonomous differential equations in an arbitrary order of perturbation theory. We prove that under certain conditions the expressions for the corrections of all orders are well defined. We also discuss the question of whether the quantum dynamics described by the derived quantum master equations is Markovian.

中文翻译：

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雷德菲尔德量子主方程的推导和 Bogoliubov 方法的修正

摘要

遵循 NN Bogoliubov 用于推导经典和量子非线性动力学方程的思想，我们推导出 Redfield 量子线性主方程，该方程广泛用于开放量子系统理论。这种方法允许人们计算系统和水库在每个时刻的联合状态，以及获得量子主方程作为扰动理论任意阶次的自主微分方程。我们证明，在一定条件下，所有阶次修正的表达式是明确定义的。我们还讨论了导出的量子主方程描述的量子动力学是否是马尔可夫的问题。