Level-spacing distributions of the Gaussian unitary random matrix ensemble

Details Level-spacing distributions of the Gaussian unitary random matrix ensemble Level-spacing distributions of the Gaussian unitary random matrix ensemble

2002-11-14

arxiv.org/abs/cond-mat/0211279v4

Phys. Stat. Sol. B 241 (2004) 2139-2147

Physics

Condensed Matter

Disordered Systems and Neural Networks

The series expansions discussed in this paper are available as Mathematica code at http://mcs.open.ac.uk/ugg2/RMT/LevelSpacing

Scientific paper

10.1002/pssb.200404784

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.

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