Quantum trajectories for Brownian motion

We present the stochastic Schrodinger equation for the dynamics of a quantu m particle coupled to a high temperature environment and apply it to the dy namics of:a driven, damped, nonlinear quantum oscillator. Apart from an ini tial slip on the environmental memory time scale, in the mean, our result r ecovers the solution of the known non-lindblad quantum Brownian motion mast er equation. A remarkable feature of our powerful stochastic approach is: i ts localization property: individual quantum trajectories remain localized wave packets for all times, even for the classically chaotic system conside red here, the localization being stronger as h -->0.