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Many-body approaches to interacting quantum systems out of equilibrium
In this presentation we will give an overview of three different many-body methods to study time-dependent quantum systems. These are the wave function based approach and two approaches based on reduced quantities, namely time-dependent density-functional theory and nonequilibrium Green's function theory. As applications we will consider the case of atoms and molecules in strong laser fields and the case of quantum transport through single molecules. We will discuss how the methods based on reduced quantities, such as the density or the Green's function, inevitably introduce correlation-induced memory into the equations. We will show how density functional theory and Green's function theory deal with this complication and give an outlook on future developments. The main intention of this presentation is to give a broader overview of the challenges one faces in a theoretical description of quantum many-body systems out of equilibrium.