Exact Non-Markovian Master Equation for Quantum Dot Decoherence via Influence Functional — E8 Intelligence Research

FINDING: Exact master equation for non-Markovian decoherence in quantum dots, derived via Feynman-Vernon influence functional, captures memory effects beyond Lindblad form. MATH: - Exact master equation: \( ρ̇(t) = -i[H_S(t),ρ] + ∑ᵢⱼ Δᵢⱼ(t)[a_j^ ρ a_i - 1/2\{a_i a_j^, ρ\}] + ∑ᵢⱼ Υᵢⱼ(t)[a_j^ ρ a_i^ - 1/2\{a_i^ a_j^, ρ\}] + h.c. \) — time-dependent coefficients \(Δᵢⱼ(t), Υᵢⱼ(t)\) encode memory kernel. - Spectral density (Ohmic): \( J(ω) = κ ω^s e-ω/ω_c \), with \(s=1\) for Ohmic, \(s<1\) sub-Ohmic, \(s>1\) super-Ohmic. - Memory kernel: \( K(t-t') = ∫_0^∞ dω J(ω) sin[ω(t-t')] \) — non-Markovian when \( K(t-t') \) decays slowly relative to system timescale. - Decoherence rate: \( Γ(t) = ∫_0^t dt' ∫_0t' dt'' K(t''-t') \) — for Ohmic bath at zero tempera Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com