Nodal structures of wave functions in chaotic billiards

The study of nodes (zeros) in waves is a subject which has been attracting attention of theoretical and experimental scientists in various areas of physics and mathematics. This includes a wide range of potential applications such as electromagnetic waves, acoustic waves, water waves, vibrating elastic plates, quantum waves etc. The theoretical studies of wave morphology and statistics of nodal structures in chaotic systems suggest that random waves may typically be a good model to describe universality in such systems under general boundary conditions [1]. This supports a previous conjecture that there might be a relation between complicated nodal structures in wave functions and the underlying classical chaotic dynamics [2]. In this presentation, the theoretical analyses adopting Gaussian-random-wave model with mixed boundary conditions are compared with numerical calculations for eigenfunctions of planar chaotic billiards. The contents presented in the following are based on the paper [3].