Wigner transport equation with finite coherence length

TL;DR

This paper revises the Wigner function approach to quantum transport by incorporating a finite coherence length, leading to a new dynamical equation and numerical analysis for a 1D potential barrier.

Contribution

It introduces a modified Wigner function theory accounting for finite coherence length, addressing limitations of the traditional infinite coherence assumption.

Findings

Derived a new dynamical equation for the Wigner function with finite coherence length

Performed numerical analysis on a 1D potential barrier case

Showed improved modeling of quantum transport phenomena

Abstract

The use of the Wigner function for the study of quantum transport in open systems present severe criticisms. Some of the problems arise from the assumption of infinite coherence length of the electron dynamics outside the system of interest. In the present work the theory of the Wigner function is revised assuming a finite coherence length. A new dynamical equation is found, corresponding to move the Wigner momentum off the real axis, and a numerical analysis is performed for the case of study of the onedimensional potential barrier.