Relaxation studies in fermion systems: Nonlinear and finite size effects

The time evolution of some non-equilibrium fermion model systems is studied by a numerical solution of the Uehling-Uhlenbeck equation in both its complete and linearized forms. The solutions are analyzed in terms of general properties of the corresponding linear eigenvalue problem. The dependence of the relaxation process on the size and the symmetry of the perturbation are investigated for spatially infinite homogeneous systems and for particles bound in an external harmonic oscillator potential as a model example for finite systems.