Spectral Decomposition in Non-Markovian Master Equations: No Golden Ratio or Base-60 Constants Found — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Spectral decomposition methods underpin non-Markovian master equations, with memory kernels encoding environment structure; no explicit golden ratio or base-60 constants appear in the listed sources. | MATH: Non-Markovian master equation: dρ(t)/dt = -i[H_S, ρ(t)] + ∫₀ᵗ K(t−s) ρ(s) ds, where K(t) is the memory kernel. Spectral decomposition: A = Σᵢ λᵢ Pᵢ (λᵢ eigenvalues, Pᵢ projectors). Feynman-Vernon influence functional yields exact time-dependent coefficients: γ(t) = ∫₀^∞ J(ω) coth(ℏω/2k_BT) sin(ωt)/ω dω (dissipation), Δ(t) = ∫₀^∞ J(ω) sin(ωt) dω (noise), with J(ω) = spectral density. | CONNECTION: None found in the provided sources. No 0.382, 0.618, 0.786, 1.618, 2.618, base-60, or crystallographic symmetries are mentioned. The spectral decomposition is linear-algebraic (eigenvalues/projectors), not harmonic-ratio-based. | DEPTH: 3 — The findings are standard mathematical physics (spectral theory applied to open quantum systems). The memory kernel is a convolution integral, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204905183
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