Abstract
For ten years, the Boltzmann equation (with some modifications to take into account some quantum effects) has been the basis of models for the description of heavy ion reactions; these models have the common feature that they simulate the Boltzmann equation (under various names as: Landau-Vlasov, Boltzmann-Uehling-Uhlenbeck, Boltzmann-Nordheim...) rather than they solve it explicitly. This report presents the basic numerical principles of the Boltzmann models in Heavy Ion Physics and their links with other modelizations of the N -Body Problem used in other fields of Physics. It discusses their validity and some applications arbitrarily chosen among the most relevant ones.
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