论文标题
使用远程相关性的混沌光谱中缺失水平数量估计的准确性和精度
Accuracy and precision of the estimation of the number of missing levels in chaotic spectra using long-range correlations
论文作者
论文摘要
我们研究了通过远程相关性估算观察到水平$φ$ $φ$ $φ$的准确性和精度。我们专注于主要统计数据，该统计数据已得出了缺少级别的比例，Dyson和Mehta的$Δ_3$以及$Δ_N$统计量的功率谱。我们使用高斯正交集合矩阵的对角线化使用蒙特卡洛模拟，并随机取出以符合公式的确定级别，并计算估计器的分布，以估计频谱的不同尺寸和$φ$的值。需要执行$Δ_n$统计量的功率谱的适当平均，以避免估计中的系统错误。一旦正确平均，即使对于最低的尺寸，我们认为$ d = 100 $的最低维度，观察到的水平的估计对于两种方法的精度也很高。但是，与使用$Δ_3$统计量的估计相比，使用$Δ_n$的功率谱的估计通常更好。对于更大的维度，这种差异显然更大。我们的结果表明，仔细分析估计集合分布的拟合价值是必须理解其实际意义并给出现实误差间隔的必要条件。
We study the accuracy and precision for estimating the fraction of observed levels $φ$ in quantum chaotic spectra through long-range correlations. We focus on the main statistics where theoretical formulas for the fraction of missing levels have been derived, the $Δ_3$ of Dyson and Mehta and the power spectrum of the $δ_n$ statistic. We use Monte Carlo simulations of the spectra from the diagonalization of Gaussian Orthogonal Ensemble matrices with a definite number of levels randomly taken out to fit the formulas and calculate the distribution of the estimators for different sizes of the spectrum and values of $φ$. A proper averaging of the power spectrum of the $δ_n$ statistic needs to be performed for avoiding systematic errors in the estimation. Once the proper averaging is made the estimation of the fraction of observed levels has quite good accuracy for the two methods even for the lowest dimensions we consider $d=100$. However, the precision is generally better for the estimation using the power spectrum of the $δ_n$ as compared to the estimation using the $Δ_3$ statistic. This difference is clearly bigger for larger dimensions. Our results show that a careful analysis of the value of the fit in view of the ensemble distribution of the estimations is mandatory for understanding its actual significance and give a realistic error interval.
