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

TL;DR

This paper establishes a formal connection between the Floquet scattering matrix and the Keldysh Green's function formalism for noninteracting quantum transport under time-periodic driving, providing a translation formula and validating fundamental identities.

Contribution

It introduces a translation formula linking Floquet scattering matrices to Green's functions and proves that this representation satisfies key transport identities.

Findings

Derived a Fourier transform-based expression for the Floquet scattering matrix.

Proved the representation satisfies fundamental transport identities.

Presented an adiabatic approximation for dc-current within the Keldysh formalism.

Abstract

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.