Statistical description of multiple collisions in the Fermi-Ulam model

Abstract

The Fermi-Ulam model consists of a point particle colliding elastically between two hards walls, one is considered fixed and the other one oscillates periodically in time. Most investigations on this model are based on a map approach that, although it is extremely efficient from the computational point of view, ignores processes which are relevant for a thorough dynamical description. The map approach considers the so called static wall approximation. In this paper, by efficiently solving the exact Fermi-Ulam model, we statistically characterize multiple collisions with the moving wall (processes not considered in the static wall approximation) and prove that structures emerging from such collisions have fractal features exhibiting self-similar characteristics.