TY - JOUR
T1 - A Mathematical Account of the NEGF Formalism
AU - Cornean, Decebal Horia
AU - Moldoveanu, Valeriu
AU - Pillet, Claude-Alain
PY - 2018/2/1
Y1 - 2018/2/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85037703583&partnerID=8YFLogxK
U2 - 10.1007/s00023-017-0638-2
DO - 10.1007/s00023-017-0638-2
M3 - Journal article
SN - 1424-0637
VL - 19
SP - 411
EP - 442
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 2
ER -