基于具有non-Markovian特性的关于量子系统约化密度矩阵的精确系统动力学方程, 分别根据方程所具有的非封闭、 不等时、积分微分方程的特性,通过Born逼近和Markov逼近得到关于量子系统约化密度矩阵的封闭、 等时和微分的Markovian主方程;逐一分析了Markovian主方程的Lindblad形式、具有方便检验正定性的GKS表达形式、 针对单量子位系统的Bloch球表达形式和无需明确的环境信息也能对开放系统进行描述的Kraus表达形式;分析 并比较了能去除系统动力学方程non-Markovian特性的4种Markov逼近方法以及其他四种特定情形下常见的Markovian主方程; 对于不适用于Markov逼近的情形,分析了能满足开放量子系统动力学对于系统状态要求的post-Markovian主方程; 当热浴与量子系统发生能量交换,且热浴与量子系统组成的封闭系统能量守恒时,给出了热浴状态不恒定时 开放量子系统的动力学方程,并通过Markov逼近得到Markovian主方程。

Based on the exact non-Markovian system dynamic equation about the reduced density matrix of quantum system, which is a non-closed, unequal in time, integral-differential equation, a closed, equal in time, differential Markovian master equation was derived about the reduced density matrix of quantum system by means of Born approximation and Markov approximation. The Lindblad form of the Markovian master equation, GKS expression for the convenience of testing positivity, Bloch sphere expression for single qubit system, Kraus expression describing dissipative quantum system without specific information of environment were analyzed respectively. Four kinds of Markov approximations that can remove the non-Markovian property were compared. The post-Markovian master equation was analyzed that can meet the perfect requirements of dissipative dynamic when the Markov approximation is not suitable to the open quantum system. When energy exchange existed between the heat bath and quantum system, and the total system composed of the bath and the quantum system has a conservation of energy, the dynamic equation of open quantum system was presented when the bath does not have a constant state, and the Markovian master equation was derived by the Markov approximation.