Dynamical Correlations for Circular Ensembles of Random Matrices

Details Dynamical Correlations for Circular Ensembles of Random Matrices Dynamical Correlations for Circular Ensembles of Random Matrices

2002-08-22

arxiv.org/abs/cond-mat/0208430v1

Physics

Condensed Matter

Statistical Mechanics

LaTeX, 20 pages, no figure

Scientific paper

Circular Brownian motion models of random matrices were introduced by Dyson and describe the parametric eigenparameter correlations of unitary random matrices. For symmetric unitary, self-dual quaternion unitary and an analogue of antisymmetric hermitian matrix initial conditions, Brownian dynamics toward the unitary symmetry is analyzed. The dynamical correlation functions of arbitrary number of Brownian particles at arbitrary number of times are shown to be written in the forms of quaternion determinants, similarly as in the case of hermitian random matrix models.

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