Non-Markovian Gaussian dissipative stochastic wave vector

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Abstract
We give a complete characterization of the stochastic wave formalism when color Gaussian fluctuations are assumed. It is shown that in this case there is only one possible generalization of the stochastic wave dynamics, which is given by the “non-Markovian quantum state diffusion model” [Phys. Rev. A 58, 1699 (1998)]. Using functional techniques, we found an equivalent evolution in terms of the stochastic propagator. From this equation any controlled approximation can be constructed. The mean density-matrix evolution is given in a closed form. A relation with quantum master equations is established. An interaction parameter expansion and a small correlation time expansion are developed.