Minimal Stochastic Model for Fermi's Acceleration

Details Minimal Stochastic Model for Fermi's Acceleration Minimal Stochastic Model for Fermi's Acceleration

2003-07-07

arxiv.org/abs/cond-mat/0307139v2

Phys. Rev. Lett., vol.92, 040601 (2004)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevLett.92.040601

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. $P(|{\bf x}|,t) = 1/t^{\nu_x}F_x(|{\bf x}|/t^{\nu_x})$ and similarly for velocity.

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