Floquet-Drude conductivity

A generalization of the Drude conductivity for systems which are exposed to periodic driving is presented. The probe bias is treated perturbatively by using the Kubo formula, whereas the external driving is included nonperturbatively using the Floquet theory. Using a different type of four-times Green functions disorder is approached diagrammatically, yielding a fully analytical expression for the Floquet-Drude conductivity. Furthermore, the Floquet Fermi ``golden rule'' is generalized to $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Floquet states, connecting the Floquet-Dyson series with scattering theory for Floquet states. It is shown that a low-energy approximation like the parabolic one fails significantly to give the correct conductivity in a system under driving.