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

André L. P. Livorati1,2, Tiago Kroetz3, Carl P. Dettmann2, Iberê L. Caldas4, and Edson D. Leonel1

  • 1Departamento de Física, UNESP, Universidade Estadual Paulista, Av. 24A 1515, Bela Vista, 13506-900, Rio Claro, SP, Brazil
  • 2School of Mathematics, University of Bristol, Bristol, BS8 1TW, United Kingdom
  • 3Departamento Acadêmico de Física, Universidade Tecnológica Federal do Paraná UTFPR, Campus Pato Branco, 85503-390, Pato Branco, PR, Brazil
  • 4Instituto de Física, IFUSP, Universidade de São Paulo, USP Rua do Matão Tr.R 187, Cidade Universitária, 05314-970, São Paulo, SP, Brazil

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Phys. Rev. E 97, 032205 – Published 9 March, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.032205

Abstract

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 noninteracting 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 midrange velocity.

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Phys. Rev. E 97, 032205– Published 9 March, 2018
  • Received 17 October 2017
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