Santhanam M S, Bandyopadhyay Jayendra N, Angom Dilip
Physical Research Laboratory, Navrangpura, Ahmedabad 380 009, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jan;73(1 Pt 2):015201. doi: 10.1103/PhysRevE.73.015201. Epub 2006 Jan 6.
The fluctuations in the quantum spectrum could be treated like a time series. In this framework, we explore the statistical self-similarity in the quantum spectrum using the detrended fluctuation analysis (DFA) and random matrix theory (RMT). We calculate the Hausdorff measure for the spectra of atoms and Gaussian ensembles and study their self-affine properties. We show that DFA is equivalent to the Delta3 statistics of RMT, unifying two different approaches. We exploit this connection to obtain theoretical estimates for the Hausdorff measure.
量子谱中的涨落可以被当作一个时间序列来处理。在此框架下，我们使用去趋势涨落分析（DFA）和随机矩阵理论（RMT）来探索量子谱中的统计自相似性。我们计算了原子谱和高斯系综的豪斯多夫测度，并研究了它们的自仿射性质。我们表明DFA等同于RMT的Delta3统计量，从而统一了两种不同的方法。我们利用这种联系来获得豪斯多夫测度的理论估计。
