Composed ensembles of random unitary matrices

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, , Citation Marcin Pozniak et al 1998 J. Phys. A: Math. Gen. 31 1059 DOI 10.1088/0305-4470/31/3/016

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1 Instytut Matematyki, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-057, Cracow, Poland

2 Instytut Fizyki im. M. Smoluchowskiego, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-057, Cracow, Poland

3 Centrum Fizyki Teoretycznej, Polska Akademia Nauk, al. Lotników 32/46, 02-668, Warsaw, Poland

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  1. Received 20 June 1997

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0305-4470/31/3/1059

Abstract

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.

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