An expansion of the master equation with applications to coupled atom-radiation systems

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Abstract
A straightforward extension of time-dependent quantum-mechanical perturbation theory is made to obtain the equivalent formulae for a statistical mixture of states. The 'master equation' resulting from this procedure is, in its lowest order, the analogue in quantum statistics of the 'Golden Rule' for transition rates and reduces exactly to this form in the limit of pure initial states. The authors give results to fourth order and illustrate their use by applying them to the problem of the resonant interaction of an electromagnetic field and a two-level atom.