标题： GUE两点关联和簇函数的数值模拟 显示英文标题

标题： Numerical Simulation of GUE Two-Point Correlation and Cluster Functions

摘要： 从delta函数的定义出发，直接对高斯酉系综（GUE）的两点本征值相关性和簇函数进行了数值模拟。 这些模拟与从三个关于两点GUE簇函数的解析公式得出的解析结果进行了比较：(i) Wigner用埃尔米特多项式表示的精确公式，(ii) Brezin和Zee的近似公式，该公式适用于分离度足够小的点，(iii) French、Mello和Pandey的近似公式，该公式适用于分离度足够大的点的平均情况。 发现如果用于表示delta函数的函数的宽度足够小，则数值模拟能够再现公式(i)和(ii)中的振荡；而当宽度增加时，公式(iii)的非振荡行为得到接近。 显示英文摘要

摘要： 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.