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In this paper we present a method to derive an exact master equation for abosonic system coupled to a set of other bosonic systems, which plays the roleof the reservoir, under the strong coupling regime, i.e., without resorting toeither the rotating-wave or secular approximations. Working with phase-spacedistribution functions, we verify that the dynamics are separated in theevolution of its center, which follows classical mechanics, and its shape,which becomes distorted. This is the generalization of a result by Glauber, whostated that coherent states remain coherent under certain circumstances,specifically when the rotating-wave approximation and a zero-temperaturereservoir are used. We show that the counter-rotating terms generatefluctuations that distort the vacuum state, much the same as thermalfluctuations.Finally, we discuss conditions for non-Markovian dynamics.

An exact master equation for the system-reservoir dynamics under the strong coupling regime and non-Markovian dynamics