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A Mathematical Account of the NEGF Formalism

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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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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Aalborg University, Skjernvej 4A, 9220, Aalborg, Denmark

    Horia D. Cornean

  2. National Institute of Materials Physics, P.O. Box MG-7 , Bucharest-Magurele, Romania

    Valeriu Moldoveanu

  3. Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France

    Claude-Alain Pillet

Authors
  1. Horia D. Cornean
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  2. Valeriu Moldoveanu
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  3. Claude-Alain Pillet
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Correspondence to Claude-Alain Pillet.

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Communicated by Jan Derezinski.

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Cornean, H.D., Moldoveanu, V. & Pillet, CA. A Mathematical Account of the NEGF Formalism. Ann. Henri Poincaré 19, 411–442 (2018). https://doi.org/10.1007/s00023-017-0638-2

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  • DOI: https://doi.org/10.1007/s00023-017-0638-2

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