论文标题
GUE两点相关和群集功能的数值模拟
Numerical Simulation of GUE Two-Point Correlation and Cluster Functions
论文作者
论文摘要
高斯单位合奏（GUE）的两点特征值相关性和群集函数的数值模拟直接从其定义上根据Deltas函数进行。将模拟与分析结果进行了比较，分析结果是从三个分析式簇函数的三个分析公式进行的：（i）Wigner的精确公式根据Hermite多项式，（II）Brezin和Zee的近似公式，该公式有效，该公式适用于具有足够小的分离和（III）法式，Mello和Pandey的近似公式的分离，对分离有效，这是有效的。发现公式（i）和（ii）中存在的振荡如果用于表示三角洲函数的函数的宽度足够小，并且随着宽度的增加而接近公式（iii）的非振荡行为，则将通过数值模拟再现。
Numerical simulations of the two-point eigenvalue correlation and cluster functions of the Gaussian unitary ensemble (GUE) are carried out directly from their definitions in terms of deltas functions. The simulations are compared with analytical results which follow from three analytical formulas for the two-point GUE cluster function: (i) Wigner's exact formula in terms of Hermite polynomials, (ii) Brezin and Zee's approximate formula which is valid for points with small enough separations and (iii) French, Mello and Pandey's approximate formula which is valid on average for points with large enough separations. It is found that the oscillations present in formulas (i) and (ii) are reproduced by the numerical simulations if the width of the function used to represent the delta function is small enough and that the non-oscillating behaviour of formula (iii) is approached as the width is increased.
