On Dissipative Features of the Vlasov Equation.: I. Relaxation in Vlasov Dynamics

We analyse the dissipative features exhibited by numerical simulations of the Vlasov equation with self-consistent mean-fields. We show both from a formal and from a numerical point of view that the system relaxes towards a classical Boltzmann distribution. In the case of fermions this implies loss of the quantal or at least semi-classical Pauli exclusion principle, contrarily to what would be naively expected from the equation itself. This effect is at least to be traced back to a numerical dissipation through the test particle method. An application to a typical case encountered in nuclear physics is presented. This relaxation effect should play a crucial role in the description of heavy-ion collisions performed with means of Boltzmann-like kinetic equation. The Vlasov dissipation in that case compete with the physical Boltzmann relaxation. We show that associated time scales indeed overlap for typical values of the parameters of the calculation.