Minimal Stochastic Model for Fermi's Acceleration

The study of a minimal stochastic model providing a description for Fermi's acceleration mechanism was presented. The analytical treatment of the model via a linear Boltzmann equation described the Fermi's acceleration mechanism. The stochastic system under study was able to generate anomalous diffusion for both position and velocity, for which the asymptotic probability distribution functions (PDFs) were derived. The diffusion process was found to be highly non-Gaussian, with the anomalous process being characterized by the PDF's scaling behavior.