Dictionary 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 non-equilibrium 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 tran sport theory. We also present the ``adiabatic'' approximation to the dc-current in the language of the Keldysh formalism. 
Liliana Arrachea and Michael Moskalets