Riccardo Adami, Rodolfo Figari, Domenico Finco, Alessandro Teta
On the asymptotic dynamics of a quantum system composed by heavy and 
light particles
(104K, Latex2e)

ABSTRACT.  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 Schroedinger group. 
Exploiting the asymptotic formula, it is also outlined an application to 
the problem of the decoherence effect produced on a heavy particle by the 
interaction with the light ones.