Spectral properties of hierarchical pseudo-Hermitian operators: numerical evidence for convergence to the critical line
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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2026
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| _version_ | 1866901802678484992 |
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| author | Savenkov, Roman |
| author_facet | Savenkov, Roman |
| contents | <p>We investigate spectral properties of a family of finite-dimensional <br>pseudo-Hermitian operators constructed on hierarchical fractal graphs. <br>Numerical analysis reveals systematic convergence of the spectrum to <br>the critical line ℜ(s) = 1/2 as the system dimension increases, <br>with machine-precision agreement observed for systems of order 10^4 vertices. <br>The limiting spectral statistics agree with predictions of random matrix <br>theory for the Gaussian Symplectic Ensemble. Connections to the <br>Hilbert-Polya conjecture and quantum chaos are discussed.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18926528 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Spectral properties of hierarchical pseudo-Hermitian operators: numerical evidence for convergence to the critical line Savenkov, Roman spectral theory, pseudo-Hermitian operators, fractal graphs, quantum chaos, random matrix theory <p>We investigate spectral properties of a family of finite-dimensional <br>pseudo-Hermitian operators constructed on hierarchical fractal graphs. <br>Numerical analysis reveals systematic convergence of the spectrum to <br>the critical line ℜ(s) = 1/2 as the system dimension increases, <br>with machine-precision agreement observed for systems of order 10^4 vertices. <br>The limiting spectral statistics agree with predictions of random matrix <br>theory for the Gaussian Symplectic Ensemble. Connections to the <br>Hilbert-Polya conjecture and quantum chaos are discussed.</p> |
| title | Spectral properties of hierarchical pseudo-Hermitian operators: numerical evidence for convergence to the critical line |
| topic | spectral theory, pseudo-Hermitian operators, fractal graphs, quantum chaos, random matrix theory |
| url | https://doi.org/10.5281/zenodo.18926528 |