Extremal spacings between eigenphases of random unitary matrices and their tensor products
Mathematical Physics
2013-11-13 v5 math.MP
Chaotic Dynamics
Quantum Physics
Abstract
Extremal spacings between eigenvalues 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.
Keywords
Cite
@article{arxiv.1204.3023,
title = {Extremal spacings between eigenphases of random unitary matrices and their tensor products},
author = {Marek Smaczynski and Tomasz Tkocz and Marek Kus and Karol Zyczkowski},
journal= {arXiv preprint arXiv:1204.3023},
year = {2013}
}