Exact stochastic simulation of dissipation and non-Markovian effects in open quantum systems

The exact dynamics of a system coupled to an environment can be described by an integro-differential stochastic equation on its reduced density. The environment influence is incorporated through a mean-field which is both stochastic and non-local in time and where the standard two-times correlation functions of the environment appear naturally. Since no approximation is made, the presented theory incorporate exactly dissipative and non-Markovian effects. Applications to the spin-boson model coupled to a heat-bath either in the weak and strong coupling limit show that the presented stochastic theory can be a valuable tool to simulate exactly the dynamics of open quantum systems. Links with Stochastic Schroedinger Equations method and possible extensions to "imaginary time" propagation are discussed