Research on models of open quantum system interacted with bath

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.