Convolutionless non-markovian master equations and quantum trajectories: Brownian motion

The use of convolutionless non-Markovian stochastic Schrödinger equations as a tool for the derivation of convolutionless master equations for non-Markovian open quantum systems, was investigated. The exact convolutionless non-Markovian master equation for the quantum Brownian motion (QBM) was also derived, in order to study the application of the stochastic equations. The key element for the derivation was a Heisenberg operator approach to the non-Markovian stochastic Schrödinger equation. The results show the way to establish the direct connection between the exact convolutionless master equation (QBM) and the corresponding convolutionless exact stochastic Schrödinger equation.