Stochastic description of quantum open systems: Formal solution and strong dissipation limit

The Caldeira-Leggett model is studied in the stochastic description. The formal solution for the random density matrix of the system as well as its average is developed and a natural explanation of the Markovian approximation is given. It is shown that the system in strong dissipation moves more like a free Brownian particle, perturbed by the potential of the system. This observation allows us to successfully derive the corresponding master equation.