A mathematical account of the NEGF formalism

TL;DR

This paper rigorously establishes the mathematical foundations of the NEGF formalism for open quantum systems, deriving key formulas and identities without relying on perturbative or complex-time techniques.

Contribution

It provides a non-perturbative, mathematically rigorous derivation of the NEGF formalism and the Jauho-Meir-Wingreen formula, avoiding traditional complex-time methods.

Findings

Rigorous derivation of the NEGF formalism

Non-perturbative proof of the Jauho-Meir-Wingreen formula

Construction of the self-energy using Volterra operators

Abstract

The main goal of this paper is to put on solid mathematical grounds the so-called Non-Equilibrium Green's Function (NEGF) transport formalism for open systems. In particular, we derive the Jauho-Meir-Wingreen formula for the time-dependent current through an interacting sample coupled to non-interacting leads. Our proof is non-perturbative and uses neither complex-time Keldysh contours, nor Langreth rules of 'analytic continuation'. We also discuss other technical identities (Langreth, Keldysh) involving various many body Green's functions. Finally, we study the Dyson equation for the advanced/retarded interacting Green's function and we rigorously construct its (irreducible) self-energy, using the theory of Volterra operators.