Statistical properties of the quantized energy spectrum of a Hamiltonian system with classically regular and chaotic trajectories: A numerical study of level-spacing distributions for two-dimensional coupled Morse-oscillator systems

Abstract

A quantification of the degree of classical chaos manifested in the quantized energy spectra of two–degree-of-freedom coupled Morse-oscillator systems with sufficiently dense energy levels is attempted by use of Brody’s repulsion parameter which characterizes his nearest-neighbor level-spacing distribution function. A close relationship is established numerically between the mass-ratio dependence of the Brody parameter and that of the relative area of the chaotic regions on the Poincaré surfaces of section in the corresponding classical system. It is shown that in the strong-coupling limit the distribution appears to tend to the Mehta-Gaudin distribution from the random matrix theory, suggesting that in this limit it is almost impossible to distinguish between the quantized version of the classical K system and those of other systems with a fairly small number of regular trajectories. The present analysis also demonstrates that the Brody parameter serves as a useful indicator for measuring the degree of mode coupling and for detecting an isolated local mode in the system.