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Annales Henri Poincaré

, Volume 19, Issue 2, pp 411–442 | Cite as

A Mathematical Account of the NEGF Formalism

  • Horia D. Cornean
  • Valeriu Moldoveanu
  • Claude-Alain Pillet
Article

Abstract

The main goal of this paper is to put on solid mathematical grounds the so-called non-equilibrium Green’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 ‘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.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Horia D. Cornean
    • 1
  • Valeriu Moldoveanu
    • 2
  • Claude-Alain Pillet
    • 3
  1. 1.Department of Mathematical SciencesAalborg UniversityAalborgDenmark
  2. 2.National Institute of Materials PhysicsBucharest-MagureleRomania
  3. 3.Aix Marseille UnivUniversité de Toulon, CNRS, CPTMarseilleFrance

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