On the time evolution of large systems: A soluble model with two-body interactions

We study the time evolution of a large system consisting of two kinds of particles that can be transformed into each other by an external field. The introduction of strong enough two-body interactions leads to the emergence of two time scales. The first one is connected with (small) asymptotic oscillations, and the second characteristic time describes a monotonic decay of the initial state. We also solve exactly and study a second model in which the two-body forces are replaced by a pair-production interaction.