Mixed-phase space of an active particle in experimental lemon billiards

Abstract

We experimentally investigated active particle-environment interactions in lemon billiards. To achieve this, we develop an Arduino robot to interact with the billiard table, which acts as our active particle, and control the shape of the lemon billiard with a parameter γ∈[0,0.5]. We experimentally confirm that the system's dynamics continuously change from regular γ=0 to fully chaotic γ=0.5, passing through cases of mixed-phase space for intermediate values of γ. We also analyze the robot's sensitivity to the initial conditions using the phase space as a function of time and the Lyapunov exponent to characterize the dynamics observed through the robot-environment interaction. Furthermore, we introduced a methodology based on recurrence analysis to compare numerical data with experimental data on a dynamical system. Numeric analyses complement the experimental results, showing a significant concordance. Our experimental setup presents an alternative method for measuring mixed-phase spaces in a billiard system outside the scope of optical physics. The robot-environment interaction provides an excellent alternative platform for experimental studies in physical systems, including additional aspects of chaos and dynamical systems, such as confined self-propelled particles and self-avoiding active particles.