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 stochas tic state vectors. They were applied first to quantum optical situatio ns. 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 numeri cal evaluation of the formal solution of those master equations requir es indeed Monte Carlo integration. The use of this method, familiar in many branches of science, leads directly to the so called quantum jum p algorithms. We develop a more convenient terminology for their descr iption. It is based on Monte Carlo theory and clarifies the formal dif ference between the Monte Carlo approach and stochastic differential e quations. In addition some new algorithms concerning the 'purity' of t he density matrix and the calculation of correlation functions are der ived. Finally we discuss the physical meaning of the stochastic state vectors briefly.