2*2 random matrix ensembles with reduced symmetry: From Hermitian to PT-symmetric matrices
Abstract
A possibly fruitful extension of conventional random matrix ensembles is proposed by imposing symmetry constraints on conventional Hermitian matrices or parity-time- (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, half-Gaussian distribution, distributions interpolating between GOE (Gaussian Orthogonal Ensemble) distribution and half Gaussian distributions, as well as 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 "truncated-GUE" statistics.
Keywords
Cite
@article{arxiv.1204.6126,
title = {2*2 random matrix ensembles with reduced symmetry: From Hermitian to PT-symmetric matrices},
author = {Jiangbin Gong and Qing-hai Wang},
journal= {arXiv preprint arXiv:1204.6126},
year = {2015}
}