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

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

2007-03-07

arxiv.org/abs/cond-mat/0703185v1

Physics

Condensed Matter

Other Condensed Matter

10 pages, 7 figures

Scientific paper

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.

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