| Summary: | 碩士 === 國立臺灣大學 === 物理研究所 === 94 === Quantum entangled states play a crucial role in the quantum teleportation and quantum information science, hence the research of the dynamics of entanglement has
become an important topic and has attracted much attention recently. We use perturbative method to derive non-Markovian master equations, which were derived in
the literature before by other extra approximations such as rotating-wave and Markovian approximations, of four different but related models of the open nanomechanical
systems respectively. Markovian approximation is close to physical phenomena only under the long time regime so we use the non-Markovian instead of Markovian approximation
to deal with our models. We use two-mode squeezed vacuum state as our initial entangled state and use the definition of logarithmic negativity to quantify the
degree of entanglement. We find that the dynamics of quantum entanglement varies periodically or maintains constant under environment free condition. However, under
the influence of environment, entanglement will decrease with time and the periodic or revival behaviors dies out gradually. As the interaction between the environment
and system increases, the time span during which entanglement exists decrease. We find that the entanglement can be sustained much longer when two subsystems are coupled to a common bath than respectively to independent reservoirs. Furthermore, we find that a separable state can become entangled through the interaction of two subsystems or coupling to a common bath. We also find that under some conditions
(e.g. at low temperature or low system vibration frequency) Markovian and rotatingwave approximations are not the good approximations. So non-Markovian case is
essential in order to obtain the accurate results of the system''s entanglement time evolution.
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