Non-Markovian quantum dynamics: Correlated projection superoperators and   Hilbert space averaging
  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. 
Heinz-Peter Breuer, Jochen Gemmer, Mathias Michel