Dissipative behavior of a quantum system interacting with a macroscopic medium

The modified Coleman-Hepp (AgBr) model describes the interaction between an ultrarelativistic quantum mechanical particle Q and an N-spin array D (a macroscopic medium in the N --> infinity limit). We prove that the energy operator for D essentially behaves as a Wiener process in the weak-coupling, macroscopic limit, in a restricted state space. No assumptions are made on the spectrum of the Hamiltonian of the macroscopic system D. The mechanism of appearance of such a stochastic process and its relevance to issues like dissipation and irreversibility are briefly discussed.