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arXiv · 1204.6126

2*2 random matrix ensembles with reduced symmetry: From Hermitian to PT-symmetric matrices

Jiangbin Gong·Qing-hai Wang
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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.

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Jiangbin Gong, Qing-hai Wang. 2012-04-27. 2*2 random matrix ensembles with reduced symmetry: From Hermitian to PT-symmetric matrices. https://doi.org/10.1088/1751-8113%2F45%2F44%2F444014

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