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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Detaljer

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.
OriginalsprogEngelsk
TidsskriftAnnales Henri Poincare
Volume/Bind19
Tidsskriftsnummer2
Sider (fra-til)411-442
Antal sider32
ISSN1424-0637
DOI
StatusUdgivet - feb. 2018
PublikationsartForskning
Peer reviewJa
ID: 266140735