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

机译：二维和三维耦合四次振荡器的水平统计特性的数值分析

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摘要

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 Poincare surface of sections of three-dimensional systems are discussed.
机译：对二维和三维量子耦合四次振荡器的光谱统计特性，即最近邻间距分布，光谱刚度和模式波动分布（MFD）进行了数值研究。通过更改单个参数，系统可以从可积分系统连续转换为混沌系统。截断的哈密顿矩阵的对角线化方法被证明对计算量子光谱是有效的。发现MFD对系统的可集成性比其混乱性更为敏感。讨论了三维系统截面的庞加莱表面。

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