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Title: 2 × 2 random matrix ensembles with reduced symmetry: From Hermitian to PT-symmetric matrices
Authors: Gong, J. 
Wang, Q.-H. 
Issue Date: 9-Nov-2012
Citation: Gong, J., Wang, Q.-H. (2012-11-09). 2 × 2 random matrix ensembles with reduced symmetry: From Hermitian to PT-symmetric matrices. Journal of Physics A: Mathematical and Theoretical 45 (44) : -. ScholarBank@NUS Repository.
Abstract: A possibly fruitful extension of conventional random matrix ensembles is proposed by imposing symmetry constraints on conventional Hermitian matrices or paritytime (PT )-symmetric matrices. To illustrate the main idea, we first study 2 × 2 complex Hermitian matrix ensembles with O(2)-invariant constraints, yielding novel level-spacing statistics such as singular distributions, the half-Gaussian distribution, distributions interpolating between the GOE (Gaussian orthogonal ensemble) distribution and half-Gaussian distributions, as well as the gapped-GOE distribution. Such a symmetry-reduction strategy is then used to explore 2 × 2 PT -symmetric matrix ensembles with real eigenvalues. In particular, PT -symmetric random matrix ensembles with U(2) invariance can be constructed, with the conventional complex Hermitian random matrix ensemble being a special case. In two examples of PT - symmetric random matrix ensembles, the level-spacing distributions are found to be the standard GUE (Gaussian unitary ensemble) statistics or the truncated- GUE statistics. © 2012 IOP Publishing Ltd.
Source Title: Journal of Physics A: Mathematical and Theoretical
ISSN: 17518113
DOI: 10.1088/1751-8113/45/44/444014
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