Instituto de Ciencias Básicas e Ingeniería, Universidad Autónoma del Estado de Hidalgo, Pachuca 42184, Hidalgo, Mexico.
Posgrado en Ciencias Naturales e Ingeniería, Universidad Autónoma Metropolitana Cuajimalpa, 05348 CDMX, Mexico.
Phys Rev E. 2018 Aug;98(2-1):022110. doi: 10.1103/PhysRevE.98.022110.
Recently, singular value decomposition (SVD) was applied to standard Gaussian ensembles of random-matrix theory to determine the scale invariance in spectral fluctuations without performing any unfolding procedure. Here, SVD is applied directly to the β-Hermite ensemble and to a sparse matrix ensemble, decomposing the corresponding spectra in trend and fluctuation modes. In correspondence with known results, we obtain that fluctuation modes exhibit a crossover between soft and rigid behavior. In this way, possible artifacts introduced applying unfolding techniques are avoided. By using the trend modes, we perform data-adaptive unfolding, and we calculate traditional spectral fluctuation measures. Additionally, ensemble-averaged and individual-spectrum averaged statistics are calculated consistently within the same basis of normal modes.
最近，奇异值分解（SVD）被应用于随机矩阵理论的标准高斯系综中，以确定谱涨落中的标度不变性，而无需执行任何展开过程。在这里，SVD 被直接应用于β-埃尔米特系综和稀疏矩阵系综，将相应的谱分解为趋势和波动模式。与已知的结果相对应，我们发现波动模式表现出软行为和硬行为之间的交叉。通过这种方式，可以避免应用展开技术引入的伪影。通过使用趋势模式，我们进行数据自适应展开，并计算传统的谱涨落度量。此外，在相同的正态模基础上，一致地计算了系综平均和单谱平均统计数据。
