none

　In this thesis, we analyze the stability of entanglement under evolution. With quantum electrodynamics which is the fundamental theory of matter and field interaction, we calculate the two-electron scattering process which is one of the main process for current generation of spin entanglement. The analysis on the generation of spin entanglement and the disentanglement effect under evolution of identical particles are presented. The stability of spin singlet state is concluded to the order of v^2/c^2. Furthermore, we turn to another physical system, cavity QED, to discuss the disentanglement effect and the generation of entanglement through spontaneous emission. The finite time generation of entanglement and dynamical suppression of disentanglement have been presented for the system with two atoms in a cavity. The comparisons with two atom being in separate cavities are also discussed. The important of the singlet state is also concluded which strengthens the results from the QED analysis. By using the so-called detuned Dicke model, we point out the incomplete relation between quantum phase transition and the discontinuity of the concurrence. The rigorous proof on the sequential instability of ground state transition for two-atom system is also presented in this thesis.

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