Electronic interactions in quantum dots within the Keldsyh formalism

Abstract

Within the Keldysh formalism, we consider electron transport through single-level quantum dots, and revisit the proper self-energy diagram up to quadratic terms in the Coulomb interaction. Convolutions of Green's functions in real energy domain are analyzed in terms of retarded and advanced, lesser and greater, time-ordered and anti-time-ordered components. By virtue of the multipole expansion of the Fermi functions and other elaborations, we provide elegant and fully analytic expressions for the various components of the bubble diagram, with promise of deeper insight on the many-body effects in biased devices.