Scattering matrix approach to the description of quantum electron transport

Abstract: We consider the scattering matrix approach to quantum electron transport in meso- and nano-conductors. This approach is an alternative to the more conventional kinetic equation and Green's function approaches, and often is more efficient for coherent conductors (especially for proving general relations) and typically more transparent. We provide a description of both time-averaged quantities (for example, current-voltage characteristics) and current fluctuations in time -- noise, as well as full counting statistics of charge transport in a finite time. In addition to normal conductors, we consider contacts with superconductors and Josephson junctions.