Abul-Magd A Y
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 2):066207. doi: 10.1103/PhysRevE.71.066207. Epub 2005 Jun 22.
We apply Tsallis' q -indexed entropy to formulate a nonextensive random matrix theory, which may be suitable for systems with mixed regular-chaotic dynamics. The joint distribution of the matrix elements is given by folding the corresponding quantity in the conventional random matrix theory by a distribution of the inverse matrix-element variance. It keeps the basis invariance of the standard theory but violates the independence of the matrix elements. We consider the subextensive regime of q more than unity in which the transition from the Wigner to the Poisson statistics is expected to start. We calculate the level density for different values of the entropic index. Our results are consistent with an analogous calculation by Tsallis and collaborators. We calculate the spacing distribution for mixed systems with and without time-reversal symmetry. Comparing the result of calculation to a numerical experiment shows that the proposed nonextensive model provides a satisfactory description for the initial stage of the transition from chaos towards the Poisson statistics.
我们应用Tsallis的q指数熵来构建一种非广延随机矩阵理论，该理论可能适用于具有混合规则 - 混沌动力学的系统。矩阵元素的联合分布是通过用逆矩阵元素方差的分布对传统随机矩阵理论中的相应量进行折叠得到的。它保持了标准理论的基不变性，但违反了矩阵元素的独立性。我们考虑q大于1的亚广延区域，预计在该区域会开始从维格纳统计向泊松统计的转变。我们计算了不同熵指数值下的能级密度。我们的结果与Tsallis及其合作者的类似计算结果一致。我们计算了具有和不具有时间反演对称性的混合系统的间距分布。将计算结果与数值实验进行比较表明，所提出的非广延模型为从混沌向泊松统计转变的初始阶段提供了令人满意的描述。
