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

TL;DR

This paper investigates the transition from normal to ballistic diffusion in a one-dimensional impact system with a bouncing ball, analyzing how accelerator modes influence transport properties and velocity dynamics.

Contribution

It introduces a detailed characterization of the transition between diffusion regimes in a bouncing ball system, highlighting the role of accelerator modes and velocity-dependent transport.

Findings

Identification of a transition point between normal and ballistic diffusion regimes.

Presence of accelerator modes leading to ballistic velocity growth.

Evidence of competition between normal and ballistic transport at intermediate velocities.

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 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.