  This article concerns the time-dependent Hartree-Fock (TDHF) approximation of
single-particle dynamics in systems of interacting fermions. We find that the
TDHF approximation is accurate when there are sufficiently many particles and
the initial many-particle state is any Gibbs equilibrium state for
noninteracting fermions (with Slater determinants as a special example).
Assuming a bounded two-particle interaction, we obtain a bound on the error of
the TDHF approximation, valid for short times. We further show that the error
of the TDHF approximation vanishes at all times in the mean field limit.
