Redfield Theory of Photosynthetic Exciton Transport: Coherence-Dissipation Optimization — E8 Intelligence Research

FINDING: Redfield theory describes photosynthetic exciton transport as a time-local Markovian master equation where coherence and dissipation compete to optimize transfer efficiency | MATH: H = Σᵢ εᵢ|i⟩⟨i| + Σᵢⱼ Jᵢⱼ|i⟩⟨j| (Frenkel exciton); dρ/dt = -i[H,ρ] + R[ρ]; R_ij,kl = Γ_ij,kl δ_kl - δ_ij Σₘ Γₘₘ,kl (Redfield tensor); Markov approximation requires τ_bath ≪ τ_system | CONNECTION: Excitonic coupling Jᵢⱼ ∝ r⁻³ (dipole-dipole), producing lattice-dependent transfer pathways; near-unity efficiency observed in pigment-protein complexes with quasi-degenerate energy levels | DEPTH: 7 FINDING: Long-lived quantum coherences in photosynthetic complexes persist at physiological temperature, contradicting simple decoherence models | MATH: Coherence lifetime τ_coh ~ 300–600 fs at 300K; dephasing rate γ_φ = γ_φ⁰ + aT + bT² (phonon scattering); oscillatory signals in 2D electronic spectroscopy follow beat frequencies ω_ij = (εᵢ - εⱼ)/ℏ | CONNECTION: Beat frequencies correspond to eigenvalue gaps o Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com