dorsal/arxiv
View SchemaGaussian-random Ensembles of Pseudo-Hermitian Matrices
| Authors | Zafar Ahmed |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407154 |
| URL | https://arxiv.org/abs/quant-ph/0407154 |
| DOI | 10.1023/B:CJOP.0000043999.11289.a3 |
Abstract
Attention has been brought to the possibility that statistical fluctuation properties of several complex spectra, or, well-known number sequences may display strong signatures that the Hamiltonian yielding them as eigenvalues is PT-symmetric (Pseudo-Hermitian). We find that the random matrix theory of pseudo-Hermitian Hamiltonians gives rise to new universalities of level-spacing distributions other than those of GOE, GUE and GSE of Wigner and Dyson. We call the new proposals as Gaussian Pseudo-Orthogonal Ensemble and Gaussian Pseudo-Unitary Ensemble. We are also led to speculate that the enigmatic Riemann-zeros (${1 \over 2}\pm i t_n)$ would rather correspond to some PT-symmetric (pseudo-Hermitian) Hamiltonian.
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"abstract": "Attention has been brought to the possibility that statistical fluctuation\nproperties of several complex spectra, or, well-known number sequences may\ndisplay strong signatures that the Hamiltonian yielding them as eigenvalues is\nPT-symmetric (Pseudo-Hermitian). We find that the random matrix theory of\npseudo-Hermitian Hamiltonians gives rise to new universalities of level-spacing\ndistributions other than those of GOE, GUE and GSE of Wigner and Dyson. We call\nthe new proposals as Gaussian Pseudo-Orthogonal Ensemble and Gaussian\nPseudo-Unitary Ensemble. We are also led to speculate that the enigmatic\nRiemann-zeros (${1 \\over 2}\\pm i t_n)$ would rather correspond to some\nPT-symmetric (pseudo-Hermitian) Hamiltonian.",
"arxiv_id": "quant-ph/0407154",
"authors": [
"Zafar Ahmed"
],
"categories": [
"quant-ph"
],
"doi": "10.1023/B:CJOP.0000043999.11289.a3",
"title": "Gaussian-random Ensembles of Pseudo-Hermitian Matrices",
"url": "https://arxiv.org/abs/quant-ph/0407154"
},
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