On the asymptotic dynamics of a quantum system composed by heavy and light particles

We consider a non-relativistic quantum system consisting of K heavy and N light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential alpha V. No interaction is assumed among particles of the same kind. Choosing an initial state in a product form and assuming alpha sufficiently small we characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. In the case K = 1 the result is extended to arbitrary alpha. The proof relies on a perturbative analysis and exploits a generalized version of the standard dispersive estimates for the Schrodinger group. Exploiting the asymptotic formula, an application to the problem of the decoherence effect produced on a heavy particle by the interaction with the light ones is also outlined.