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

TL;DR

This paper investigates the influence of the Pauli Exclusion Principle on the many-electron Wigner function across various scenarios, revealing exchange effects, equilibrium distributions, and interaction dynamics in phase space.

Contribution

It provides a comprehensive analysis of the Pauli principle's effects on the Wigner function in different physical situations, including scattering, equilibrium, and interactions.

Findings

Exchange and correlation holes in phase space

Wigner function approaches a Fermi distribution in equilibrium

Two-particle interactions are essential for accurate transport modeling

Abstract

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.