dorsal/arxiv
View SchemaA pseudo-unitary ensemble of random matrices, PT-symmetry and the Riemann Hypothesis
| Authors | Zafar Ahmed, Sudhir R. Jain |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407167 |
| URL | https://arxiv.org/abs/quant-ph/0407167 |
Abstract
An ensemble of 2 x 2 pseudo-Hermitian random matrices is constructed that possesses real eigenvalues with level-spacing distribution exactly as for the Gaussian Unitary Ensemble found by Wigner. By a re-interpretation of Connes' spectral interpretation of the zeros of the Riemann zeta function, we propose to enlarge the scope of search of the Hamiltonian connected with the celebrated Riemann Hypothesis by suggesting that the Hamiltonian could also be PT-symmetric (or pseudo-Hermitian).
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"abstract": "An ensemble of 2 x 2 pseudo-Hermitian random matrices is constructed that\npossesses real eigenvalues with level-spacing distribution exactly as for the\nGaussian Unitary Ensemble found by Wigner. By a re-interpretation of Connes\u0027\nspectral interpretation of the zeros of the Riemann zeta function, we propose\nto enlarge the scope of search of the Hamiltonian connected with the celebrated\nRiemann Hypothesis by suggesting that the Hamiltonian could also be\nPT-symmetric (or pseudo-Hermitian).",
"arxiv_id": "quant-ph/0407167",
"authors": [
"Zafar Ahmed",
"Sudhir R. Jain"
],
"categories": [
"quant-ph"
],
"title": "A pseudo-unitary ensemble of random matrices, PT-symmetry and the Riemann Hypothesis",
"url": "https://arxiv.org/abs/quant-ph/0407167"
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