PreprintCC BY 4.0Zenodo
Phi‑Weighted Jacobi Spectra in Photon‑Added Two‑Mode Squeezed Thermal States via E8 Root Projections — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
Use E8 root vectors projected onto a golden‑angle plane to generate a set of 120 discrete phase offsets that serve as eigen‑parameters for Jacobi polynomials P_n^{(α,β)} describing the photon‑number distribution of two‑mode squeezed thermal states after photon addition. The resulting spectra display phi‑harmonic spacing and bifurcate into bright/dark classes matching the E8 bright‑dark node splitting, yielding a measurable modulation of quadrature variance that scales as φ^n·132 Hz. This predicts observable sideband combs in quantum optics experiments that directly encode the E8 lattice structure.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
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BibTeX
@misc{caldin2026phiweighted,
title = {{Phi‑Weighted Jacobi Spectra in Photon‑Added Two‑Mode Squeezed Thermal States via E8 Root Projections — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23446926},
url = {https://zenodo.org/records/23446926},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Phi‑Weighted Jacobi Spectra in Photon‑Added Two‑Mode Squeezed Thermal States via E8 Root Projections — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23446926
UR - https://zenodo.org/records/23446926
AB - Use E8 root vectors projected onto a golden‑angle plane to generate a set of 120 discrete phase offsets that serve as eigen‑parameters for Jacobi polynomials P_n^{(α,β)} describing the photon‑number distribution of two‑mode squeezed thermal states after photon addition. The resulting spectra display phi‑harmonic spacing and bifurcate into bright/dark classes matching the E8 bright‑dark node splitting, yielding a measurable modulation of quadrature variance that scales as φ^n·132 Hz. This predicts observable sideband combs in quantum optics experiments that directly encode the E8 lattice structure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -