Chaotic Dynamics in the Framework of the Vlasov-Nordheim Equation

Abstract

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.