Effect of the Pauli Exclusion Principle in the Many-Electron Wigner Function

An analysis of the Wigner function for identical particles is presented. Four situations have been considered. i) A scattering process between two indistinguishable electrons described by a minimum uncertainty wave packets showing the exchange and correlation hole in Wigner phase space. ii) An equilibrium ensemble of N electrons in a one-dimensional box and in a one-dimensional harmonic potential showing that the reduced single particle Wigner function as a function of the energy defined in the Wigner phase-space tends to a Fermi distribution. iii) The reduced one-particle transport-equation for the Wigner function in the case of interacting electrons showing the need for the two-particle reduced Wigner function within the BBGKY hierarchy scheme. iv) The electron-phonon interaction in the two-particle case showing co-participation of two electrons in the interaction with the phonon bath.