A general description of the Quantum Trajectories is presented, both from the Montecarlo and Stochastic Schrodinger equation viewpoint. Also a physical interpretation of these trajectories is given. The example is a mode of the electromagnetic field in a cavity interacting with a beam of two or three level atoms, the field playing the role of the small system and the atomic beam standing for a reservoir at finite temperature. We show that the evolution of the field states, under continuous monitoring of the state of the atom which leave the cavity can be described with the Monte-Carlo method or a diffusion equation, depending on the configuration of the system.
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