Correlated projection superoperators in relaxation and transport investigations

The time-convolutionless (TCL) projection operator technique allows a systematic analysis of the dynamical properties of open quantum systems. Unfortunately, using the standard projector to investigate the decay to equilibrium fails to describe the dynamics of a small system coupled to a finite environment correctly. However, a recently introduced correlated projection operator leads to the appropriate dynamical behavior and shows a reasonable good agreement with the exact Schrodinger dynamics. Furthermore, a similar projector can be used to describe the transport through a quantum system. Using the technique in Fourier space allows for a detailed analysis of transport in the context of its length scale dependence as well. Finally, the method is also applicable to realistic systems, e. g., spin models.