Nodal Domain Distribution for a Nonintegrable Two-Dimensional Anharmonic Oscillator

We investigate the transition from integrable to chaotic dynamics in the quantum mechanical wave functions from the point of view of the nodal structure by employing a two dimensional quartic oscillator. We find that the number of nodal domains is drastically reduced as the dynamics of the system changes from integrable to nonintegrable, and then gradually increases as the system becomes chaotic. The number of nodal intersections with the classical boundary as a function of the level number shows a characteristic dependence on the dynamics of the system, too. We also calculate the area distribution of nodal domains and study the emergence of the power law behavior with the Fisher exponent in the chaotic limit.