The Wigner function for electron transport in mesoscopic systems

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 Eights separated by scattering processes like semiclassi cal particles. A Monte Carlo algorithm can be developed, based on such Wign er paths. Furthermore, a two-time Green function G can be used to define a Wigner function where momentum and energy are treated as independent variab les. The same Monte Carlo approach would then also yield the spectral funct ion for the electron interacting with the phonon gas.