Hyperacceleration in a stochastic Fermi-Ulam model

Details Hyperacceleration in a stochastic Fermi-Ulam model Hyperacceleration in a stochastic Fermi-Ulam model

2006-10-27

arxiv.org/abs/nlin/0610068v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 3 figures. To be published in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.97.194102

Fermi acceleration in a Fermi-Ulam model, consisting of an ensemble of particles bouncing between two, infinitely heavy, stochastically oscillating hard walls, is investigated. It is shown that the widely used approximation, neglecting the displacement of the walls (static wall approximation), leads to a systematic underestimation of particle acceleration. An improved approximative map is introduced, which takes into account the effect of the wall displacement, and in addition allows the analytical estimation of the long term behavior of the particle mean velocity as well as the corresponding probability distribution, in complete agreement with the numerical results of the exact dynamics. This effect accounting for the increased particle acceleration -Fermi hyperacceleration- is also present in higher dimensional systems, such as the driven Lorentz gas.

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