DYNAMICAL EQUATION AND MONTE CARLO SIMULATION OF THE TWO-TIME WIGNER FUNCTION FOR ELECTRON QUANTUM TRANSPORT

Within the Wigner-function formalism for electron quantum transport in semiconductors a two-time Wigner function is defined starting from the Green-function formalism. After a proper Fourier transform a Wigner function depending on p and W as independent variables is obtained. This new Wigner function extends the Wigner formalism to the frequency domain and carries information related to the spectral density of the system. A Monte Carlo approach based on the generation of Wigner paths, already developed for the single-time Wigner function, has been extended to evaluate the momentum and energy-dependent Wigner function. Results will be shown for electrons subject to the action of an external field and in presence of scattering with optical phonons