  The transient signals derived from femtosecond pump-probe experiments are
analyzed in terms of the coherent evolution of the energy levels perturbed by
the excitation pulse. The model system is treated as the sum of independent
two-level subsystems that evolve adiabatically or are permanently excited,
depending on the detuning from the central wavelength of the excitation laser.
This approach will allow us to explain numerically and analytically the
convergence between the coherent and incoherent (rate equations) treatments for
complex multi-level systems. It will be also shown that the parameter that
determines the validity of the incoherent treatment is the distribution of
states outside and inside the laser bandwidth, rather than the density of
states as it is commonly accepted.
