title: Extremal spacings between eigenphases of random unitary matrices and their tensor products.
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=n(k) becomes large, the nearest neighbor distribution P(s) becomes Poissonian, but statistics of extreme spacings P(s(min)) and P(s(max)) reveal certain deviations from the Poissonian behavior.
authors: Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Cracow, Poland.
authors: Marek
authors: M
authors: Smaczyński
authors: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom.
authors: Tomasz
authors: T
authors: Tkocz
authors: Center of Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland.
authors: Marek
authors: M
authors: Kuś
authors: Center of Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland and Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Cracow, Poland.
authors: Karol
authors: K
authors: Życzkowski