Abul-Magd AY, Simbel MH
Faculty of Science, Zagazig University, Zagazig, Egypt.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Oct;62(4 Pt A):4792-8. doi: 10.1103/physreve.62.4792.
We apply some of the methods that have been successfully used to describe the nearest-neighbor-spacing distributions of levels of systems with mixed regular-chaotic dynamics to the calculation of high-order spacing distributions. The distributions for chaotic spectra are described in terms of a previously suggested generalization of Wigner's surmise, which assumes that the high-order level repulsion function is given by a product of the zero-order ones and that all of the spacing distributions are nearly Gaussian functions at large spacings. We compare the expressions obtained by the different methods for the next-nearest-neighbor spacing distribution with the outcome of a recently published numerical experiment on systems in transition between order and chaos. We show that the evolution of the shape of that distribution during the transition of the system from a chaotic to a regular regime is slower than the corresponding transition for the nearest-neighbor spacing distribution.
我们将一些已成功用于描述具有混合规则 - 混沌动力学系统能级的最近邻间距分布的方法应用于高阶间距分布的计算。混沌谱的分布是根据先前提出的维格纳推测的推广来描述的，该推广假设高阶能级排斥函数由零阶排斥函数的乘积给出，并且在大间距时所有间距分布几乎都是高斯函数。我们将通过不同方法得到的次近邻间距分布的表达式与最近发表的关于处于有序和混沌过渡阶段系统的数值实验结果进行比较。我们表明，在系统从混沌状态转变为规则状态的过程中，该分布形状的演变比最近邻间距分布的相应转变要慢。
