Linear response theory for a highly excited system far from equilibrium

In this paper a generalization of Kubo's linear response theory is treated for systems which are driven far off equilibrium by external fields. The reduced density operator is calculated by a time-dependent projector technique in a fast moving reference frame. The response of the system with respect to a second retarded probe pulse is considered which reflects the higher complexity of the corresponding equations in comparison with Kubo's linear response theory. The response of a virtually excited exciton system to a white probe pulse is discussed for a highly excited semiconductor in the athermal stage and in the low density limit. The poles of the two-particle Green's functions contain the differences of time-dependent shifted quasi particle energies. This behavior reflects the dynamic renormalization of the band structure as the laser induced gap creation or the dynamic Stark effect.