On Kinetic Equations in Heavy-Ion Physics

We present the theoretical foundations of the dynamical approaches used in heavy-ion collisions at beam energies of some tens of MeV per nucleon. After a brief review of mean field (TDHF) and Intra nuclear Cascade approaches we consider Boltzmann-like kinetic equations, adapted to the nuclear context. Simulations of these equations (BUU, VUU, ...) are widely used in this field of physics. We show how to obtain this kind of equations in a nuclear context and we discuss the formal difficulties raised by these equations. In a second part we consider alternative descriptions, such as stochastic extensions of these kinetic equations or molecular dynamics models. We present several models (MD,QMD, ...) of this kind and discuss their limitations. In a last part we discuss the ability of the approaches introduced in the previous parts to fulfill Pauli exclusion principle. We show the difficulties raised by this principle, as well in the case of simulations of kinetic equations as in molecular dynamics models. We conclude by introducing fermionic molecular dynamics (FMD, AMD) methods, which are directly linked to TDHF, and a stochastic extension of TDHF (STDHF)