Level statistics and eigenfunctions of square torus billiards: Manifesting the transition from regular to chaotic behaviors

Abstract

We thoroughly analyze the level statistics and eigenfunctions in concentric as well as nonconcentric square torus billiards. We confirm the characteristics of quantum and classical correspondence and the existence of scarred and superscarred modes in concentric square torus billiards. Furthermore, we not only verify that the transition from regular to chaotic behaviors can be manifested in nonconcentric square torus billiards, but also develop an analytical distribution to excellently fit the numerical level statistics. Finally, we intriguingly observe that numerous eigenstates commonly exhibit the wave patterns to be an ensemble of classical diamond trajectories, as the effective wavelengths are considerably shorter than the size of internal hole.