Wigner paths and boundary conditions for electron transport in open systems with electron-phonon interaction

A Wigner-function approach to the study of quantum transport in open systems in the presence of phonon scattering is presented. Two important issues are discussed: a) the existence of Wigner paths in phase space with many analogies with the semiclassical description of transport and b) how to deal with boundary conditions for the analysis of real open structures. Theoretical and computational results are discussed in view of the application of this formalism to the simulation of transport in mesoscopic structures.