1994•Journal of Physics A Mathematical and GeneralRequires access

Random unitary matrices

Karol Życzkowski, Marek Kuś

Abstract

Methods of constructing random matrices typical of circular unitary and circular orthogonal ensembles are presented. We generate numerically random unitary matrices and show that the statistical properties of their spectra (level-spacing distribution, number variance) and eigenvectors (entropy, participation ratio, eigenvector statistics) confer to the predictions of the random-matrix theory, for both CUE and COE.

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Key concepts: Circular ensemble, Random matrix, Unitary state, Unitary matrix, Mathematics, Circular law, Eigenvalues and eigenvectors, Entropy (arrow of time)