The Generalization of Wave Chaos to Nonlinear Systems

The wave properties of systems that show chaos in the classical limit, and are large compared to the wavelength, are extensively studied in the field of wave chaos. These systems are quite common in life, ranging from the small scale of atomic nuclei, to mesoscopic quantum systems like quantum dots, to macroscopic acoustic and microwave resonators (billiards), optical systems, and even to ocean waves in the sea. Many of the statistical properties of linear over-moded classical and quantum billiards have been successfully understood utilizing concepts from quantum/wave chaos. As an example, the Random Coupling Model (RCM) incorporates the universal fluctuations predicted by random matrix theory, and the system-specific features, to give a comprehensive description of wave scattering data on real-life linear wave chaotic systems [1]-[4]. We now wish to explore the wave chaotic properties of nonlinear systems. Many questions arise, such as whether or not universal statistical properties will be seen in such systems. We have begun experiments and simulations to explore the statistical properties of such nonlinear billiards.