A Mathematical Account of the NEGF Formalism

A Mathematical Account of the NEGF Formalism

Publication Type:

Journal Article

Source:

Annales Henri Poincare, Volume 19, Issue 2, p.411-442 (2018)

ISBN:

1424-0637

Abstract:

<p>The main goal of this paper is to put on solid mathematical grounds the so-called non-equilibrium Green&#39;s function 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 &#39;analytic continuation.&#39; We also discuss other technical identities (Langreth, Keldysh) involving various many-body Green&#39;s functions. Finally, we study the Dyson equation for the advanced/retarded interacting Green&#39;s function and we rigorously construct its (irreducible) self-energy, using the theory of Volterra operators.</p>