  Consider a system of $N$ particles interacting through Newton's second law
with Coulomb interaction potential in one spatial dimension or a
$\mathcal{C}^2$ smooth potential in any dimension. We prove that in the mean
field limit $N \to + \infty$, the $N$ particles system displays instabilities
in times of order $\log N$ for some configurations approximately distributed
according to unstable homogeneous equilibria.
