A mathematical account of the NEGF formalism

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.

arXiv commentAnnales Henri Poincaré 2017

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• Sparsity pattern of the self-energy for classical and quantum impurity problems
• A Dyson equation for non-equilibrium Green's functions in the partition-free setting
• On Three "Anomalous" Measurements of Nonlinear QPC Conductance
• Emergence of the 2nd Law in an Exactly Solvable Model of a Quantum Wire