Transition from normal to ballistic diffusion in a one-dimensional impact system

Andre Livorati, Tiago Kroetz, Carl Dettmann, Ibere L Caldas, Edson D Leonel

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)
268 Downloads (Pure)


We characterize a transition from normal to ballistic diffusion in a bouncing ball dynamics. The system is composed of a particle, or an ensemble of non-interacting particles, experiencing elastic collisions with a heavy and periodically moving wall under the influence of a constant gravitational field. The dynamics lead to a mixed phase space where chaotic orbits have a free path to move along
the velocity axis, presenting a normal diffusion behavior. Depending on the control parameter, one can observe the presence of featured resonances, known as accelerator modes, that lead to a ballistic growth of velocity. Through statistical and numerical analysis of the velocity of the particle, we are able to characterize a transition between the two regimes, where transport properties were used to characterize the scenario of the ballistic regime. Also, in an analysis of the probability of an orbit to reach an accelerator mode as a function of the velocity, we observe a competition between the normal and ballistic transport in the mid range velocity.
Original languageEnglish
Article number032205
JournalPhysical Review E
Issue number3
Publication statusPublished - 9 Mar 2018

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