Time evolution of entangled biatomic states in a cavity

We study the time evolution of entangled states of a pair of identical atoms, considered in the harmonic approximation, coupled to an environment represented by an infinite set of free oscillators, with the whole system confined within a spherical cavity of radius $R$. Taking the center-of-mass and the relative-position coordinates, and using the dressed-state approach, we present the time evolution of some quantities measuring the entanglement, for both limits of a very large and a small cavity; the chosen examples are simple and illustrate these very distinct behaviors.