Perturbative expansion for master equation and it applications

We construct generally applicable small-loss rate expansions for the density operator of an open system. Successive terms of those expansions yield characteristic loss rates for dissipation processes. Three applications are presented in order to give further insight into the context of those expansions. The first application, of a two-level atom coupling to a bosonic environment, shows the procedure and the advantage of the expansion, whereas the second application that consists of a single mode field in a cavity with linewidth $\kappa$ due to partial transmission through one mirror illustrates a practical use of those expansions in quantum measurements, and the third one, for an atom coupled to modes of a lossy cavity shows the another use of the perturbative expansion.Comment: 10 pages, 1 figur