Scattering problems involving electrons, photons, and Dirac fermions

Abstract

The theoretical foundation for the work reported here is provided by Landauer's scattering theory of electron transport. The three main ingredients of a scattering problem are (1) a set of reservoirs that emit and absorb particles, (2) the particles themselves, that propagate as waves between the reservoirs and (3) a scatterer that obstructs free propagation. In this thesis two classes of problems are considered. The first class results when the physical quantities characterizing the reservoirs or the scatterer are not constant in time. The second class results when wave propagation is described by the Dirac equation rather than the Schroedinger equation, as is the case in a 2D form of carbon, called graphene.