Refined evaluation of the level-spacing distribution of symplectic ensembles: Moments and implications

Abstract

To obtain a more precise value for the variance ?2 of the joint probability distribution of a symplectic ensemble, we extend previous numerical evaluations of a power series. Our result ?2?0.1041 shows that the excellent approximation using the analytically simple Wigner surmise fractionally overestimates this value. This behavior is important in establishing the trend of a generalization of the surmise to describe the terrace-width distribution on vicinal surfaces. We also obtain precise estimates of the skewness and the kurtosis of the exact distribution, as well as the related moments.