The calculation of the equilibrium optical properties of bulk silicon by
using the Bethe--Salpeter equation solved in the Kohn--Sham basis represents a
cornerstone in the development of an ab--initio approach to the optical and
electronic properties of materials. Nevertheless calculations of the {\em
transient} optical spectrum using the same efficient and successful scheme are
scarce. We report, here, a joint theoretical and experimental study of the
transient reflectivity spectrum of bulk silicon. Femtosecond transient
reflectivity is compared to a parameter--free calculation based on the
non--equilibrium Bethe--Salpeter equation. By providing an accurate description
of the experimental results we disclose the different phenomena that determine
the transient optical response of a semiconductor. We give a parameter--free
interpretation of concepts like bleaching, photo--induced absorption and
stimulated emission, beyond the Fermi golden rule. We also introduce the
concept of optical gap renormalization, as a generalization of the known
mechanism of band gap renormalization. The present scheme successfully
describes the case of bulk silicon, showing its universality and accuracy.Comment: 14 pages, 13 figure
