Hyperprojectors and master equations for quantum dynamical maps

The widely used approaches for the derivation of quantum master equations are based on projection methods which lead to Nakajima-Zwanzig master equations or time-convolutionless master equations and their perturbative approximations. Our results are based on such methods, but we apply them to the dynamical maps instead of density matrices. In particular, we use projection operators which map superoperators to superoperators, so we call them "hyperprojectors". In this talk we discuss a very simple hyperprojector, which corresponds to the averaging with respect to fast free dynamics. One of obvious advantages of such an approach is that the initial conditions are always consistent with such a hyperprojector. Using such an approach, we obtain second order master equations and their Bogolubov-van Hove limit. We also consider an analog of stroboscopic limit for such a hyperprojector. This work was funded by Russian Federation represented by the Ministry of Science and Higher Education (grant number 075-15-2020-788).