Three-Dimensional Quartic Oscillators for the Study of Mode Fluctuation Distribution

Abstract

The mode fluctuation distribution (MFD) of three-dimensional quartic oscillators coupled by quartic perturbations is numerically studied. The system is continuously transferred from the integrable to the chaotic regime by changing a single coupling strength. The MFD of the three-dimensional systems is found to be a sensitive measure of integrability as in two-dimensional systems. If the system is exactly integrable, the MFD has the characteristic skew distribution. On the other hand, even in the region that the chaotic and integrable volumes are comparable in the phase space, the MFD already becomes almost the Gaussian distribution as in the completely chaotic regime. We also find that the Brody parameter increases gradually without a plateau by increasing the coupling constant. It shows a clear contrast to the two-dimensional system.