Wigner-function formulation for quantum transport in semiconductors: theory and Monte Carlo approach

The Wigner-function approach to the quantum theory of electron transport in mesoscopic systems is reviewed. Delta-like or “particle” contributions to the Wigner function evolve in time along “paths” formed by ballistic free flights interrupted by scattering processes as semiclassical particles. A Monte Carlo algorithm based on such Wigner paths will be presented. It extends to quantum transport the Monte Carlo procedure that proved to be very successful for the study of semiclassical transport.