Numerical analysis of level statistical properties of two- and three-dimensional coupled quartic oscillators

Abstract

The spectral statistical properties, i.e. the nearest neighbor spacing distribution, the spectral rigidity and the mode fluctuation distribution (MFD) are numerically studied for two- and three-dimensional quantum coupled quartic oscillators. By changing a single parameter, the system is continuously transformed from an integrable system to a chaotic one. The diagonalization method of the truncated Hamiltonian matrix is shown to be effective for the calculation of quantum spectra. The MFD is found to be more sensitive to the integrability of the system than its chaoticity. The Poincaré surface of sections of three-dimensional systems are discussed.