ON A LIOUVILLE-MASTER EQUATION FORMULATION OF OPEN QUANTUM-SYSTEMS

The dynamics of open quantum systems is formulated in terms of a probability distribution on the underlying Hilbert space. Defining the time-evolution of this probability distribution by means of a Liouville-master equation the time-dependent wave function of the system becomes a stochastic Markov process in the sense of classical probability theory. It is shown that the equation of motion for the two-point correlation function of the random wave function yields the quantum master equation for the statistical operator. Stochastic simulations of the Liouville-master equation are performed for a simple example from quantum optics and are shown to be in perfect agreement with the analytical solution of the corresponding equation for the statistical operator.