Quantum Brownian motion of a heavy particle: An adiabatic expansion

We consider Brownian motion of a heavy particle (mass M), under conditions where the particle itself displays quantum effects, either because T is smaller than characteristic frequencies, or because the thermal wave packet size, h̵√MT, is bigger than characteristic lengths. A direct space method is developed which clearly separates wave packet spread from recoil effects (in the coupling to the heat bath): for a heavy particle, the latter are small, while the former are important in a quantum regime (a plain expansion in 1/M is thus precluded).