Three-dimensional quartic oscillators for the study of mode fluctuation distribution

The mode fluctuation distribution (MFD) of three-dimensional quartic oscill ators coupled by quartic perturbations is numerically studied. The system i s continuously transferred from the integrable to the chaotic regime by cha nging a single coupling strength. The MFD of the three-dimensional systems is found Co be a sensitive measure of integrability as in two-dimensional s ystems. 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 b ecomes almost the Gaussian distribution as in the completely chaotic regime . We also find that the Brody parameter increases gradually without a plate au by increasing the coupling constant. It shows a clear contrast to the tw o-dimensional system.