On the stochastic limit for quantum theory

The basic ideas of the stochastic limit for a quantum system with discrete energy spectrum, coupled to a Bose reservoir are illustrated through a detailed analysis of a general linear interaction: under this limit we have quantum noise processes substituting for the field. We prove that the usual Schrödinger evolution in interaction representation converges to a limiting evolution unitary on the system and noise space which, when reduced to system's degrees of freedom, provides the master and Langevin equations that are postulated on heuristic grounds by physicists. In addition, we give a concrete application of our results by deriving the evolution of an atomic system interacting with the electrodynamic field without recourse to either rotating wave or dipole approximations.