Projection operator techniques and Hilbert space averaging in the quantum theory of nonequilibrium systems

Abstract

The development of efficient strategies for the treatment of the dynamics of relevant observables in complex quantum systems plays a decisive role in the theory of quantum relaxation and transport behavior. Here we discuss the most important tools that are based on the projection operator techniques of nonequilibrium statistical mechanics. For both the Nakajima-Zwanzig and the time-convolutionless projection operator technique we derive the equations of motion for a set of relevant observables and develop explicit expressions in second and fourth order of the corresponding perturbation expansions. We also discuss the Hilbert space average method which is based on the idea of a best guess of conditional quantum expectations determined by an average over a suitable region in the underlying Hilbert space, and relate this method to the projection operator technique.