  By means of molecular dynamics computer simulations we investigate the out of
equilibrium relaxation dynamics of a simple glass former, a binary
Lennard-Jones system, after a quench to low temperatures. We study both one
time quantities and two-times correlation functions. Two-times correlation
functions show a strong time and waiting time $t_w$ dependence. For large $t_w$
and times corresponding to the early $\beta$-relaxation regime the correlators
approach the Edwards-Anderson value by means of a power-law in time. at long
times $\tau$ the correlation functions can be expressed as $C_{\rm
AG}(h(t_w+\tau)/h(t_w))$ and compute the function $h(t)$. This function is
found to show a $t$-dependence which is a bit stronger than a logarithm and to
depend on the observable considered.
  Finally we discuss our measurements of the time dependent response function.
We find that at long times the correlation functions and the response are not
related by the usual fluctuation dissipation theorem but that this relation is
similar to the one found for spin glasses with one step replica symmetry
breaking.
