Averaged exact dynamics of a stochastic non-Markovian wave vector

We find the exact dynamics – in mean value – for a particular model of the Schrödinger–Langevin equation that preserves norm for all realizations [J. Phys. A Math. Gen. 32 (1999) 631]. Using Novikovʹs theorem we prove that the dynamics generated by a stochastic Gaussian Hamiltonian gives for the density matrix an evolution governed by a non-local in time Kossakowki–Lindblad like generator. This model can help to study dissipation and decoherence beyond the Markovian approximation.