The quantum weak coupling limit. II: Langevin equation and finite temperature case (Q1913405)

Summary: We complete the program started in [authors, Commun. Math. Phys. 131, No. 3, 537-570 (1990; Zbl 0703.60096)] by proving that, in the weak coupling limit, the matrix elements, in the collective coherent vectors, of the Heisenberg evolved of an observable of a system coupled to a quasi-free reservoir through a laser type interaction, converge to the matrix elements of a quantum stochastic process satisfying a quantum Langevin equation driven by a quantum Brownian motion. Our results apply to an arbitrary quasi-free reservoir so, in particular, the finite temperature case is included.