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Secular determinants of random unitary matrices.

Haake, Fritz and Kus, Marek and Sommers, Hans-Jurgen and Schomerus, Henning and Zyczkowski, Karol (1996) Secular determinants of random unitary matrices. Journal of Physics A: Mathematical and General, 29. p. 3641. ISSN 1361-6447

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    Abstract

    We consider the characteristic polynomials of random unitary matrices U drawn from various circular ensembles. In particular, the statistics of the coefficients of these polynomials are studied. The variances of these `secular coefficients' are given explicitly for arbitrary dimension and continued analytically to arbitrary values of the level repulsion exponent beta. The latter secular coefficients are related to the traces of powers of U by Newton's well known formulae. While the traces tend to have Gaussian distributions and to be statistically independent among one another in the limit as the matrix dimension grows large, the secular coefficients exhibit strong mutual correlations due to Newton's mixing of traces to coefficients. These results might become relevant for current efforts at combining semiclassics and random-matrix theory in quantum treatments of classically chaotic dynamics.

    Item Type: Article
    Journal or Publication Title: Journal of Physics A: Mathematical and General
    Subjects:
    Departments: Faculty of Science and Technology > Physics
    ID Code: 712
    Deposited By: Dr Henning Schomerus
    Deposited On: 31 Oct 2007
    Refereed?: Yes
    Published?: Published
    Last Modified: 17 Sep 2013 08:23
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/712

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