We present a novel approach to the investigation of transport coefficients in condensed matter systems, which is based on a pertinent time-convolutionless (TCL) projection operator technique. In this context we analyze in advance the convergence of the corresponding perturbation expansion and the influence of the occurring inhomogeneity. The TCL method is used to establish a formalism for a consistent derivation of a Boltzmann equation from the underlying quantum dynamics, which is meant to apply to non-ideal quantum gases. We obtain a linear(ized) collision term that results as a finite non-singular rate matrix and is thus adequate for further considerations, e.g., the calculation of transport coefficients. In the work at hand we apply the provided scheme to numerically compute the diffusion coefficient of an atomic wire and especially analyze its dependence on certain model properties, in particular on the width of the wire.

The work at hand presents a novel approach to transport in closed quantum systems. To this end a method is introduced which is essentially based on projection operator techniques, in particular on the time-convolutionless (TCL) technique. The projection onto local densities of quantities such as energy, magnetization, particles, etc. yields the reduced dynamics of the respective quantities in terms of a systematic perturbation expansion. Especially, the lowest order contribution of this expansion is used as a strategy for the analysis of transport in "modular" quantum systems. The term modular basically corresponds to (quasi-) one-dimensional structures consisting of identical or at least similar many-level subunits. Modular quantum systems are demonstrated to represent many physical situations and several examples are given. In the context of these quantum systems lowest order TCL is shown as an efficient tool which also allows to investigate the dependence of transport on the considered length scale. In addition an estimation for the validity range of lowest order TCL is derived. As a first application a "design" model is considered for which a complete characterization of all available transport types as well as the transitions to each other is possible. For this model the relationship to quantum chaos and the validity of the Kubo formula is further discussed. As an example for a "real" system the Anderson model is finally analyzed. The results are partially verified by the numerical solution of the full time-dependent Schroedinger equation which is obtained by exact diagonalization or approximative integrators.