Semiclassical asymptotics of quantum stochastic equations

The time evolution of an open quantum system – a particle in a potential field under continuous observation – is described in the framework of the quantum stochastic calculus. Two types of stochastic wave equations are considered: prior, corresponding to nonselective measurements, and posterior, depending on the trajectories of selective measurements. An exactly solvable model of the measurement of the coordinates of a free particle is considered. By means of this model, the quantum Zeno paradox can be explained on the basis of the theory of posterior dynamics of the observables of open quantum systems. Semiclassical solutions are constructed for both types of quantum stochastic wave equation by a stochastic generalization of the WKB – Maslov method.