Electronic structure and transport from density matrices and density functionals

As a link between theory and experiment, computational physics has received increasingattention in the last decades. Powerful supercomputers provide the possibility of accuratecalculations for large systems, while highly advanced experimental tools allow researchers toconduct experiments on mesoscopic scale. Such developments lead to a bigger overlap areabetween these two fields of physics.On the other hand, computational approaches are based on theories that are under constantenhancement in order to obtain more accurate results, and therefore, both application andtheory development have crucial role in this field of physics. In the present dissertation, we contribute to the both parts.In the first part, we apply the density functional approach on carbon-nanotube-based systems, and we study the effect of defects addatoms, impurities, and their periodicity on the electronic transport properties of the systems. We also predict the formation of Schottky barrier in the junction between two metallic and semiconducting nanotubes. The second part is dedicated to study the challenges and difficulties in time dependent reduced density matrix approaches. We show that the current approximations make the time evolution of two-body reduced density matrix very unstable. We study the possible reasons behind such behavior, and this might lead us to more stable approximations.