On the Asymptotic Dynamics of a Quantum System Composed by Heavy and Light Particles

Details On the Asymptotic Dynamics of a Quantum System Composed by Heavy and Light Particles On the Asymptotic Dynamics of a Quantum System Composed by Heavy and Light Particles

2005-12-08

arxiv.org/abs/math-ph/0512023v1

Physics

Mathematical Physics

38 pages

Scientific paper

10.1007/s00220-006-0115-0

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 Schr\"{o}dinger 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.

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