Abstract
A theoretical Wigner-function approach to the study of quantum transport in open systems in presence of phonon scattering is presented. It is shown here that in order to solve the Wigner equation in its integral form the knowledge of the Wigner function at all points of the phase space at an initial time ${t}_{0}$ can be substituted by the knowledge of the same function inside the region of interest at ${t}_{0}$ and on its boundary at all times ${t}^{\ensuremath{'}}$ less then the observation time $t.$ The theory has been applied to calculate the current associated with electron quantum transport across given potential profiles and in presence of phonon scattering.
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