The Solutions Of Post-markovian Master Equation For Different Conditions

With the development of quantum information theory, an increasing number scholarspay close attention to the physical resources of quantum information processing. Theinevitable interactions between the quantum systems, which are the carriers of these resources,and the environment leads the systems to be regarded as open quantum systems. Thisdissertation mainly studies the solutions of the post-Markovian master equation for differentconditions in the open quantum systems.This thesis consists of three parts. The first part is composed of chapter2. In this chapter,we introduce the memory kernel master equation and the derivation of the post-Markovianmaster equation. We have presented the general theories of the solution of the post-Markovianmaster equation.Part two is composed of chapter3. In this section, we solve the Markovian masterequation by virtue of damping basis approach and solve the post-Markovian master equationfor two models which are the damping harmonic oscillator in vacuum and the dampingtwo-level system affected by squeezed thermal bath. Then we apply our solution to differentinitial states. The results show that we can deduce the Markovian master equation from thepost-Markovian master equation in the Markovian limit and when the time tends to infinitythe steady-state of the two quantum dynamical processes are the same. Afterwards wedescribe the two-level system by the Bloch sphere and analyze the evolution of the quantumstates.The third part is composed of chapter4. Here, we discuss the non-Markovianity of thequantum process. Firstly, we construct a measure for non-Markovianity which is based on thetrace distance of any two quantum states. It turned out that the Markovian process tend tocontinuously reduce the distinguishability between any two states. Otherwise, it will benon-Markovian process. Then we study the non-Markovianity of the post-Markovian process,The results show that the post-Markovian process can be classified as time-dependentMarkovian process and the distinguishability of quantum states is monotonically decreasing.Finally, the discussion and conclusions are given.