Color Dynamics In Phase Space: The Balescu-Lenard-Vlasov Approach

We propose to use the Balescu-Lenard-Vlasov (BLV) equation to describe relativistic heavy ion collisions. We use an inter-quark Richardson's potential consistent with the indications of Lattice QCD calculations. The color degrees of freedom are explicitly taken into account. We explicitly demonstrate that the Vlasov approach alone is insufficient in the hadronization region. In order to overcome this problem we prepare the initial condition for many events using molecular dynamics with frictional cooling and a Thomas-Fermi approximation to the Fermi motion. These events are averaged and propagated in time using the Vlasov approach. The fluctuations are used to evaluate the collision term and in turn the number of q-$\bar q$ created.