# A consistent approach for the treatment of Fermi acceleration in time-dependent billiards.

@article{Karlis2012ACA, title={A consistent approach for the treatment of Fermi acceleration in time-dependent billiards.}, author={Alexandros K. Karlis and Fotis K. Diakonos and Vassilios Constantoudis}, journal={Chaos}, year={2012}, volume={22 2}, pages={ 026120 } }

The standard description of Fermi acceleration, developing in a class of time-dependent billiards, is given in terms of a diffusion process taking place in momentum space. Within this framework, the evolution of the probability density function (PDF) of the magnitude of particle velocities as a function of the number of collisions n is determined by the Fokker-Planck equation (FPE). In the literature, the FPE is constructed by identifying the transport coefficients with the ensemble averages of…

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It is shown that a process with mean velocity that exhibits power-law growth in time can be analyzed using the Langevin equation with multiplicative noise and the solution to the corresponding Fokker-Planck equation is derived.

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