Truncation method for Green's functions in time-dependent fields

We investigate the influence of a time-dependent, homogeneous electric field on scattering properties of noninteracting electrons in an arbitrary static potential. We develop a method to calculate the (Keldysh) Green's function in two complementary approaches. Starting from a plane-wave basis, a formally exact solution is given in terms of the inverse of a matrix containing infinitely many ''photoblocks,'' which can be evaluated approximately by truncation. In the exact eigenstate basis of the scattering potential, we obtain a version of the Floquet state theory in the Green's-functions language. The formalism is checked for cases such as a simple model of a double barrier in a strong electric field. Furthermore, an exact relation between the inelastic scattering rate due to the microwave and the ac conductivity of the system is derived, which in particular holds near or at a metal-insulator transition in disordered systems.