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Composed ensembles of random unitary matrices

Marcin Pozniak-+, Karol Zyczkowski++ and Marek Kus§

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Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate their physical relevance. We also discuss the methods of generating random matrices distributed according to invariant Haar measure on the orthogonal and unitary group.


PACS

02.10.Yn Matrix theory

02.20.-a Group theory

05.45.Mt Quantum chaos; semiclassical methods

MSC

81Q50 Quantum chaos (See also 37Dxx)

51F25 Orthogonal and unitary groups (See also 20H05)

15A52 Random matrices

28C10 Set functions and measures on topological groups, Haar measures, invariant measures (See also 22Axx, 43A05)

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 3 (23 January 1998)

Received 20 June 1997



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