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Extremal spacings between eigenphases of random unitary matrices and their tensor products
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Smaczyński, Marek, Tkocz, Tomasz, Kuś, Marek and Życzkowski, Karol (2013) Extremal spacings between eigenphases of random unitary matrices and their tensor products. Physical Review E, Volume 88 (Number 5). Article: 052902. doi:10.1103/PhysRevE.88.052902 ISSN 1539-3755.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.88.052902
Abstract
Extremal spacings between eigenphases of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for N=4. We study ensembles of tensor product of k random unitary matrices of size n which describe independent evolution of a composite quantum system consisting of k subsystems. In the asymptotic case, as the total dimension N=nk becomes large, the nearest neighbor distribution P(s) becomes Poissonian, but statistics of extreme spacings P(smin) and P(smax) reveal certain deviations from the Poissonian behavior.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Physical Review E | ||||
Publisher: | American Physical Society | ||||
ISSN: | 1539-3755 | ||||
Official Date: | November 2013 | ||||
Dates: |
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Volume: | Volume 88 | ||||
Number: | Number 5 | ||||
Page Range: | Article: 052902 | ||||
DOI: | 10.1103/PhysRevE.88.052902 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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