Quantum chaos and level distribution in the model of two bound oscillators

A quantum model of two bound oscillators is studied under conditions when the dynamics is stochastic in the classical limit and the measure of stability islands is small. For this purpose we determine in the classical case the parameter ranges corresponding to both regular and stochastic dynamic regimes. The dependence of the Kolmogorov entropy on energy of the system is also obtained. Histograms for the distribution of separations between neighboring energy levels are presented and the characteristics of the levels spacing are determined in the quantum case. It is shown that there exists a nonmonotonic dependence of the degree of levels spacing on the dynamic parameters even at those energies for which the effect of the stability islands can be neglected