The Wigner function for electron transport in mesoscopic systems

Abstract

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 are introduced that evolve in time along `paths' formed by ballistic free flights separated by scattering processes like semiclassical particles. A Monte Carlo algorithm can be developed, based on such Wigner paths. Furthermore, a two-time Green function G< can be used to define a Wigner function where momentum and energy are treated as independent variables. The same Monte Carlo approach would then also yield the spectral function for the electron interacting with the phonon gas.