期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
卷 48, 期 38, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/48/38/38FT02
关键词
random matrix theory; PT-symmetry; quantum mechanics
资金
- Imperial College JRF scheme
- L'Oreal UNESCO Women in Science Fellowship
- Royal Society
- EPSRC DTA grant
- Engineering and Physical Sciences Research Council [1648128] Funding Source: researchfish
Recently much effort has been made towards the introduction of non-Hermitian random matrix models respecting PT-symmetry. Here we show that there is a one-to-one correspondence between complex PT-symmetric matrices and split-complex and split-quaternionic versions of Hermitian matrices. We introduce two new random matrix ensembles of (a) Gaussian split-complex Hermitian; and (b) Gaussian split-quaternionic Hermitian matrices, of arbitrary sizes. We conjecture that these ensembles represent universality classes for PT-symmetric matrices. For the case of 2 x 2 matrices we derive analytic expressions for the joint probability distributions of the eigenvalues, the one-level densities and the level spacings in the case of real eigenvalues.
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