Relation between scattering-matrix and Keldysh formalisms for quantum transport driven by time-periodic fields

We present the relation between the Floquet scattering matrix and the nonequilibrium Green's function formalisms to transport theory in noninteracting electronic systems in contact to reservoirs and driven by time-periodic fields. We present a translation formula that expresses the Floquet scattering matrix in terms of a Fourier transform of the retarded Green's function. We prove that such representation satisfies the fundamental identities of transport theory. We also present the adiabatic approximation to the dc current in the language of the Keldysh formalism.