  In the framework of the time-dependent mean field theory, we solve the
Vlasov-Nordheim equation and study the sensitive dependence of this highly
non-linear equation on the initial conditions. We find that, when nuclear
matter is inside the spinodal region, initially small differences between
similar trajectories grow exponentially and produce strongly divergent paths
resulting in a chaotic evolution. We focus on the fact that chaos spontaneously
arises without putting any additional noise. We calculate the largest Lyapunov
exponent for various initial densities. This analysis is performed for nuclear
matter in two dimensions. It is argued that the mean field chaoticity can cause
nuclear multifragmentation observed in intermediate energy heavy-ion reactions.
