Metraipolis › archive › dc_eda877df02eb

Hidden Dyson Universality in Inverse-Spectral Geometry — arXiv:2608.13475

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.13475
License (as archived): CC0-1.0
Archived: 2026-10-19T05:06:27.655Z
SHA-256 of the archived text: 326e44ed78c03941af8a9bb56fa0db6d11661d4092aa95f122d49285e3a3251d
Stable URL of this page: https://metraipolis.com/documento/dc_eda877df02eb

How to cite

Hidden Dyson Universality in Inverse-Spectral Geometry — arXiv:2608.13475 — arXiv (en), https://arxiv.org/abs/2608.13475 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_eda877df02eb (Metraipolis archive dc_eda877df02eb, sha256 326e44ed78c03941af8a9bb56fa0db6d11661d4092aa95f122d49285e3a3251d)

BibTeX

@misc{dceda877df02eb,
  title = {Hidden Dyson Universality in Inverse-Spectral Geometry — arXiv:2608.13475},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.13475},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_eda877df02eb; sha256 326e44ed78c03941af8a9bb56fa0db6d11661d4092aa95f122d49285e3a3251d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.13475. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Dyson universality typically manifests itself in local eigenvalue statistics. Here we show that its signature survives a nonlinear inverse-spectral reconstruction and reappears in the matrix geometry of the reconstructed operator. Using a dressing transformation, we map each unfolded spectrum to a deformation $f(x)$ of a fixed harmonic oscillator and represent it in the common oscillator basis by $F_{mn}=\bra m|f|n\ket$. We resolve the matrix-element weight into shells of fixed distance $d=|m-n|$, corresponding to the energy-transfer channels of the reference oscillator, and characterize the resulting distribution by distance-shell moments. Independently calibrated on Gaussian $\beta$-ensembles, these moments vary smoothly with $\beta$ and distinguish the GOE, GUE, and GSE. With this calibration fixed, applying the same diagnostic to the nontrivial zeros of the Riemann zeta function places the reconstructed operators in the GUE sector. Thus, the GUE character of the zeros is recovered not through direct statistics of the input levels, but from the distance-resolved geometry of the reconstructed operator.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-08-14 in cond-mat.stat-mech).
Categorie arXiv: Mathematical Physics (math-ph) ; Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th).
Pagina del lavoro: https://arxiv.org/abs/2608.13475 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T04:56:02.861Z dalla pagina https://arxiv.org/catchup/cond-mat.stat-mech/2026-08-14?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).