STOCHASTIC DYNAMICS OF QUANTUM JUMPS

The dynamics of an open quantum system coupled to an external reservoi r is studied on the basis of a recently proposed formulation of quantu m statistical ensembles in terms of probability distributions on proje ctive Hilbert space. The previous result is generalized to include int eraction Hamiltonians of the form Sigma(i) A(i) x B-i, where A(i) and B-i are operators acting on the Hilbert space of the reduced system an d of the reservoir, respectively. The differential Chapman-Kolmogorov equation governing the dynamics of the conditional transition probabil ity of the reduced system is derived from the underlying microscopic t heory based on the Schrodinger equation for the total system. The stoc hastic process turns out to be a piecewise deterministic Markovian jum p process in the projective Hilbert space of the reduced system. The s ample paths are derived and shown to be similar to those of the Monte Carlo wave function simulation methods proposed in the literature. Fin ally, a diffusion-noise expansion of the Liouville master equation is performed and demonstrated to yield a stochastic differential equation for the state vector of the open system.