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@article{Graefe:2015:38/38FT02,
author = {Graefe, E-M and Mudute-Ndumbe, S and Taylor, M},
doi = {38/38FT02},
journal = {Journal of Physics A: Mathematical and Theoretical},
title = {Random matrix ensembles for PT-symmetric systems},
url = {http://dx.doi.org/10.1088/1751-8113/48/38/38FT02},
volume = {48},
year = {2015}
}

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TY  - JOUR
AB  - Recently much effort has been made towards the introduction of non-Hermitianrandom matrix models respecting $PT$-symmetry. Here we show that there is aone-to-one correspondence between complex $PT$-symmetric matrices andsplit-complex and split-quaternionic versions of Hermitian matrices. Weintroduce two new random matrix ensembles of (a) Gaussian split-complexHermitian, and (b) Gaussian split-quaternionic Hermitian matrices, of arbitrarysizes. They are related to the split signature versions of the complex and thequaternionic numbers, respectively. We conjecture that these ensemblesrepresent universality classes for $PT$-symmetric matrices. For the case of$2\times2$ matrices we derive analytic expressions for the joint probabilitydistributions of the eigenvalues, the one-level densities and the levelspacings in the case of real eigenvalues.
AU  - Graefe,E-M
AU  - Mudute-Ndumbe,S
AU  - Taylor,M
DO  - 38/38FT02
PY  - 2015///
SN  - 1751-8113
TI  - Random matrix ensembles for PT-symmetric systems
T2  - Journal of Physics A: Mathematical and Theoretical
UR  - http://dx.doi.org/10.1088/1751-8113/48/38/38FT02
UR  - http://arxiv.org/abs/1505.07810v2
UR  - http://hdl.handle.net/10044/1/25500
VL  - 48
ER  -

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