Ab-initio Numerical Simulation of Quantum Transport in Materials Didier Mayou Laboratoire d'Etude des propriétés Electroniques des Solides (LEPES) CNRS- Grenoble, France   The standard model of conduction in condensed matter is the Drude model, which can be justified through the semi-classical Bloch-Boltzmann theory. Yet, in many systems of great current interest, quantum interferences occur, that are not described by the semi classical theory. These systems require a fully quantum treatment of transport. In the last few years it has become possible to perform ab-initio computations that contribute to a much better understanding of the physics of quantum transport in materials and nano-objects. Two recent examples are presented about nanotubes and complex intermetallic phases related to quasicrystals.