THE WEAK-COUPLING LIMIT WITHOUT ROTATING WAVE APPROXIMATION

We investigate the behaviour, in the weak coupling limit, of a system interacting with a Boson reservoir without assuming the rotating wave approximation, i.e. we allow the system Hamiltonian to have a finite set of characteristic frequencies rather than a single one [cf. equation (1. 4)]. Our main result is the proof that the weak coupling limit of the matrix elements with respect to suitable collective vectors of the solution of the Schrodinger equation in interaction representation (i.e. the wave operator at time t) exists and is the solution of a quantum stochastic differential equation driven by a family of independent quantum Brownian motions, one for each characteristic frequency of the system Hamiltonian.