Torres-Vargas G, Fossion R, Tapia-Ignacio C, López-Vieyra J C
Posgrado en Ciencias Naturales e Ingeniería, Universidad Autónoma Metropolitana Cuajimalpa, 05348 CDMX, Mexico.
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510 CDMX, Mexico.
Phys Rev E. 2017 Jul;96(1-1):012110. doi: 10.1103/PhysRevE.96.012110. Epub 2017 Jul 6.
We apply the singular value decomposition (SVD) method, based on normal-mode analysis, to decompose the spectra of finite random matrices of standard Gaussian ensembles in trend and fluctuation modes. We use the fact that the fluctuation modes are scale invariant and follow a power law, to characterize the transition between the extreme regular and chaotic cases. Thereby, we quantify the quantum chaos in systems described by random matrix theory in a direct way, without performing any previous unfolding procedure, and therefore, avoiding possible artifacts.
我们应用基于简正模式分析的奇异值分解（SVD）方法，将标准高斯系综的有限随机矩阵光谱分解为趋势模式和波动模式。我们利用波动模式具有尺度不变性且遵循幂律这一事实，来表征极端规则情况与混沌情况之间的转变。由此，我们以直接的方式量化随机矩阵理论所描述系统中的量子混沌，无需执行任何先前的展开程序，从而避免可能出现的伪像。
