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The population and decay evolution of a qubit under the time-convolutionless master equation

We consider the population and decay of a qubit under the electromagnetic environment. Employing the time-convolutionless master equation, we investigate the Markovian and non-Markovian behaviour of the corresponding perturbation expansion. The Jaynes-Cummings model on resonance is investigated. Some figures clearly show the different evolution behaviours. The reasons are interpreted in the paper.