Rainbows, Billiards and Chaos

Abstract

Starting at the end of last century, Chaos Theory is used to explain since the dynamics of a dripping faucet to the essence of black holes. The main aspect of this ubiquity is because chaotic systems involve nonlinear systems, and most systems behave linearly only when they are close to equilibrium, far from this region, we can observe a myriad of behaviors. We studied some phenomena involving rays and waves in optics and acoustics, such as rainbows, fogbows, Glory effect, iridescent clouds, halos and sound waves in acoustic billiards from the point of view of chaotic systems. We explore the aspects of ray splitting and their relationship with Chaos Theory, based on different subjects, such as Random Matrix Theory, Caustics, Interference and Geometrical Theory of Diffraction. One interesting case in such systems is that the existence of discontinuities or singularities can lead to wave diffraction, which is related to additional contributions to the trace formula, with the presence of creeping orbits and caustics. This approach can be extended to quantum systems, such as nuclear rainbow. We will present scattering of light in open systems and compare them to the scattering of particles. We are presenting experimental results of light scattering in a cylinder and observing the “spiral rainbow” pattern.