In this paper we provide a microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses. We single out both the differences with the phenomenological master equation used in the literature and the approximations under which the phenomenological model correctly describes the dynamics of the atom-cavity system. Some examples wherein the phenomenological and the microscopic master equations give rise to different predictions are discussed in detail.
Scala, M., Militello, B., Messina, A., Piilo, J., & Maniscalco, S. (2007). Microscopic derivation of the Jaynes-Cummings model with cavity losses. Physical Review A, 75(1), . https://doi.org/10.1103/PhysRevA.75.013811