The linear absorption can be written as a dipoledipole auto-correlation function with the ensemble averaging done over the ground state density matrix of the ensemble. For linear absorption spectroscopy, the laser strength is much weaker than the internal interaction energies of the system such that we can treat it as a perturbation. The linear response of a system to the external radiation field, in the impulsive limit, is expressed as R (1) (t 1 ) = -iTr[μ(t 1 )[μ(t 0 ), ρ(g) ]].