Minimal Stochastic Model for Fermi's Acceleration

Abstract

We introduce a simple stochastic system able to generate anomalous diffusion both for position and velocity. The model represents a viable description of the Fermi's acceleration mechanism and it is amenable to analytical treatment through a linear Boltzmann equation. The asymptotic probability distribution functions (PDF) for velocity and position are explicitly derived. The diffusion process is highly non-Gaussian and the time growth of moments is characterized by only two exponents ${\nu }_x$ and ${\nu }_v$. The diffusion process is anomalous (non Gaussian) but with a defined scaling properties i.e. $P(|\mathbf{x}|,t)=1/t^{{\nu }_x}{F}_x(|\mathbf{x}|/t^{{\nu }_x})$ and similarly for velocity.

RevTeX4, 4 pages, 2 eps-figures (minor revision)

References in corpus (2)

• Anomalous Diffusion in Infinite Horizon Billiards
• A mechanical model of normal and anomalous diffusion

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