Exact Master Equation for Non-Markovian Entangled Coherent State Decoherence — E8 Intelligence Research

FINDING: Non-Markovian decoherence of entangled coherent states is exactly solvable via Feynman-Vernon influence functional, yielding a master equation with time-dependent memory kernels — the spectral density of the environment dictates the kernel's structure, linking decoherence rates to the Fourier transform of the bath correlation function. | MATH: Exact master equation: dρ/dt = -i[H_S,ρ] - ∫₀ᵗ ds K(t-s)[X,[X,ρ(s)]] where K(t) = ∫₀^∞ dω J(ω) sin(ωt) (spectral density J(ω) = Σ g_k² δ(ω-ω_k)); for Ohmic bath J(ω) ∝ ω e^{-ω/ω_c}, kernel K(t) ∝ 1/(1+ω_c²t²) — algebraic decay, not exponential. For sub-Ohmic J(ω) ∝ ω^s (s<1), K(t) ∝ t^{-(1+s)} — long-time memory. | CONNECTION: The golden angle (137.5° = 2π/φ²) appears in the *optimal* sampling of spectral densities in quasiperiodic environments — if J(ω) is sampled at golden-ratio intervals in frequency space, the memory kernel's Fourier transform avoids aliasing, preserving self-similar structure (K(t) ∝ t^{-α} with α related to φ via α Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com