The characteristic function of optical evolution

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The master equation of quantum optical density operator is transformed to the equation of characteristic function. The parametric amplification and amplitude damping as well as the phase damping are considered. The solution for the most general initial quantum state is obtained for parametric amplification and amplitude damping. The purity of one mode Gaussian system and the entanglement of two mode Gaussian system are studied.
10 pages, 3 figures

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