MONTE-CARLO INTEGRATION OF DISSIPATIVE QUANTUM-SYSTEMS

In this paper we review some new stochastic methods designed for large dissipative quantum systems with quantum Markovian master equations. These methods approximate the density matrix by an ensemble of stochastic state vectors. They were applied first to quantum optical situations. Although it is common use in quantum optics to entitle stochastic approaches as Monte Carlo methods, this term originally was introduced for the evaluation of ordinary integrals. It is shown that the numerical evaluation of the formal solution of those master equations requires indeed Monte Carlo integration. The use of this method, familiar in many branches of science, leads directly to the so called quantum jump algorithms. We develop a more convenient terminology for their description. It is based on Monte Carlo theory and clarifies the formal difference between the Monte Carlo approach and stochastic differential equations. In addition some new algorithms concerning the 'purity' of the density matrix and the calculation of correlation functions are derived. Finally we discuss the physical meaning of the stochastic state vectors briefly.