  We formulate a time-dependent density functional theory (TDDFT) in terms of
the density matrix to study ultrafast phenomena in semiconductor structures. A
system of equations for the density matrix components, which is equivalent to
the time-dependent Kohn-Sham equation, is derived. From this we obtain a TDDFT
version of the semiconductor Bloch equations, where the electronic many-body
effects are taken into account in principle exactly. As an example, we study
the optical response of a three-dimensional two-band insulator to an external
short-time pulsed laser field. We show that the optical absorption spectrum
acquires excitonic features when the exchange-correlation potential contains a
$1/q^{2}$ Coulomb singularity. A qualitative comparison of the TDDFT optical
absorption spectra with the corresponding results obtained within the
Hartree-Fock approximation is made.
