Classical chaos and quantum level density of an anharmonic oscillator

The Liapunov exponents of two-dimension anharmonic oscillator systems are studied through numerical calculations. The result shows that the systems consist of regular and irregular regions in phase space in the classical limit. The corresponding quantum systems are investigated. The distribitionP(s) of spacings between adjacent energy levels indicates a corresponding transition from Poisson-like distribution to Wigner-like distribution.P(s) is dependent on the total irregular fraction of phase space.