Linear response for systems far off equilibrium

The Kubo theory of linear response is extended with respect to reference states, being excited far off equilibrium. Using the time dependent projector technique, generalized response functions are introduced. The structure of the corresponding evolution equations is mainly determined by the observable algebra of the relevant subspace. Generalizations of retarded Green's functions may be introduced in the limit of two well separated time scales of evolution, but generally, the energy representation becomes unsuitable in systems far off equilibrium. After a reformulation of the evolution superoperator, a transparent example of a two-level system is considered, where the exciting laser pulse has the shape of a Gaussian envelope.