Dynamics of Electrons and Ab-Initio Modeling of Quantum Transport

TL;DR

This paper introduces the Landauer formula for quantum conductance and analyzes the dynamics of establishing steady-state current, providing a physical basis for 4-point conductance related to non-local conductivity.

Contribution

It offers a simple derivation of the Landauer formula and presents a formal framework for understanding 4-point conductance in quantum transport systems.

Findings

Derived the Landauer formula using the uncertainty principle.

Analyzed the dynamics of steady-state current setup.

Established a formal relation between 4-point conductance and non-local conductivity.

Abstract

In this short paper we first give a very simple derivation of the Landauer formula for a 2-point conductance of QJ $G^{2P}$, based on the uncertainty principle. The aim of this is to introduce this central equation of quantum transport to a general audience. Next we analyse the dynamics of setting up a steady-state current in a simple many-electron system and use these observations to present physical basis and formal result for the 4-point conductance $G^{4P}$, rigorously related to the non-local conductivity of an extended system consisting of electrodes and their junction.