  We derive the general Kubo formula in a form that solely utilizes the time
evolution of displacement operators. The derivation is based on the
decomposition of the linear response function into its time symmetric and time
anti-symmetric part. We relate this form to the well-known
fluctuation-dissipation formula and discuss theoretical and numerical aspects
of it. The approach is illustrated with an analytical example for magnetic
resonance as well as a numerical example where we analyze the electrical
conductivity tensor and the Chern insulating state of the disordered Haldane
model. We introduce a highly efficient time-domain approach that describes the
quantum dynamics of the resistivity of this model with an at least 1000-fold
better performance in comparison to existing time-evolution schemes.
