Transmission Coefficient as a Three-Point Retarded Function

TL;DR

This paper presents a novel approach to calculating transmission probability in quantum transport by expressing it as a three-point retarded correlation function, utilizing Kubo formalism and Eliashberg theory.

Contribution

It introduces a new formulation of transmission probability using a three-point retarded function, providing a different perspective on transport theory.

Findings

Transmission probability expressed as a three-point retarded function.

Utilizes Kubo formalism and Eliashberg theory for analytic properties.

Offers a new viewpoint on quantum transport theory.

Abstract

We show that the transmission probability through a small interacting region connected to noninteracting leads, can be written in terms of a retarded product of a three-point correlation function defined in the real time. Our proof is based on the Kubo formalism, and uses an Eliashberg theory for analytic properties of vertex functions. The aim of this short report is to add a new viewpoint to the transport theory described in the previous paper: A.O., J. Phys. Soc. Jpn. 70 (2001) 2666.