Simple and complex formulations of quantum transport

I discuss two methods that help us to understand and predict transport properties of nanoscale systems. The first one allows us to calculate the conductance of quantum junctions by correlated first-principles ground-state techniques. I will demonstrate the performance of the technique on simple metallic junctions. The second method, based on a novel stroboscopic wavepacket basis set, offers insight and mean-field predictions of the time-dependent and non-linear behaviour for systems with applied external bias. I will discuss applications of the latter for relaxation dynamics of a switching-on process in a simple model junctions and for current induced spin polarisation in nanostructures.