  The time-convolutionless (TCL) projection operator technique allows a
systematic analysis of the non-Markovian quantum dynamics of open systems. We
introduce a class of projection superoperators which project the states of the
total system onto certain correlated system-environment states. It is shown
that the application of the TCL technique to this class of correlated
superoperators enables the non-perturbative treatment of the dynamics of
system-environment models for which the standard approach fails in any finite
order of the coupling strength. We demonstrate further that the correlated
superoperators correspond to the idea of a best guess of conditional quantum
expectations which is determined by a suitable Hilbert space average. The
general approach is illustrated by means of the model of a spin which interacts
through randomly distributed couplings with a finite reservoir consisting of
two energy bands. Extensive numerical simulations of the full Schroedinger
equation of the model reveal the power and efficiency of the method.
