Level-spacing distributions of the Gaussian unitary random matrix ensemble

TL;DR

This paper derives and computes level-spacing distributions for the Gaussian Unitary Ensemble using coupled differential equations, enabling precise comparisons with experimental and numerical data.

Contribution

It introduces a method to express GUE level-spacing distributions via coupled differential equations and provides high-order series solutions for accurate small-spacing analysis.

Findings

Series solutions up to order 50 for level-spacing distributions

Accurate description of small-spacing distribution parts

Facilitates comparison with experimental and numerical data

Abstract

Level-spacing distributions of the Gaussian Unitary Ensemble (GUE) of random matrix theory are expressed in terms of solutions of coupled differential equations. Series solutions up to order 50 in the level spacing are obtained, thus providing a very good description of the small-spacing part of the level-spacing distribution, which can be used to make comparisons with experimental or numerical data. The level-spacing distributions can be obtained by solving the system of differential equations numerically.