Non-Markovian quantum dynamics and the method of correlated projection superoperators

Efficient methods for the description of the non-Markovian dynamics of open systems play an important role in many proposed applications of quantum mechanics. Here we review some of the most important tools that are based on the projection operator techniques of nonequilibrium statistical mechanics. The standard product-state projection is generalized to a new class of correlated projection superoperators that allow the treatment of strong memory effects, and lead to a non-Markovian generalization of the Lindblad equation.