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Level‐spacing distributions of the Gaussian unitary random matrix ensemble
Author(s) -
Grimm Uwe
Publication year - 2004
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200404784
Subject(s) - circular ensemble , mathematics , unitary state , gaussian , random matrix , statistical physics , matrix (chemical analysis) , mathematical analysis , unitary matrix , distribution (mathematics) , series (stratigraphy) , differential equation , physics , quantum mechanics , eigenvalues and eigenvectors , political science , law , paleontology , materials science , composite material , biology
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. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)