Stochastic evolution of systems of particles obeying an exclusion principle

We present numerical solutions of a nonlinear Fokker-Planck equation to describe a Fermi gas. The model equation (G. Kaniadakis, P. Quarati, Phys. Rev. E 49 (1994) 5103) includes a nonlinear term due to the Pauli exclusion principle which has been disregarded up to now. A new numerical method to study the time evolution of the distribution function is presented. The method can be applied to any potential and allows us to describe accurately and efficiently a Fermi gas. In this work we focus on the differences between the results of the linear case, in which the effects of the exclusion principle are not considered, and the nonlinear case, in which these effects are taken into account.