Time-resolved Dyson equations in the context of time-dependent density-functional theory: Extension to solid systems

It is shown that under certain conditions an instantaneous resolvent G(z;t) of a time-dependent Kohn-Sham or Kohn-Sham-Dirac operator H(t) can be defined from which the particle and the magnetization density can be evaluated directly using contour integrations. The corresponding Green’s function can be evaluated within a multiple-scattering scheme by solving at each given time t coupled radial differential equations for the single-site problem. This scheme is in particular intriguing since within the adiabatic time-dependent density functional the configurational part of a time-dependent perturbation can be viewed as a contribution to an effective (full) potential. First applications are shown for an Fe atom excited by a femtosecond laser pulse.