Return to equilibrium for some quantum trajectories

Abstract

We consider the situation of a two-level quantum system undergoing a continuous indirect measurement, giving rise to so-called "quantum trajectories". We first describe these quantum trajectories in a physically realistic discrete-time setup and we then justify, by going to the continuous-time limit, the "stochastic Schr\"odinger equation" attached to this model. We prove return to equilibrium properties for these equations.