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

Abstract

FINDING: The exact master equation for quantum dot decoherence, derived via Feynman-Vernon influence functional, provides a non-Markovian generalization of Lindblad form with time-dependent coefficients — the only mathematically rigorous exact solution in this domain. | MATH: Exact master equation: \( \dot{\rho}(t) = -i[H_S(t), \rho] + \sum_{ij} \Delta_{ij}(t) [2 f_j \rho f_i^\dagger - \{f_i^\dagger f_j, \rho\}] \) where \(\Delta_{ij}(t)\) are time-dependent dissipation coefficients (non-Markovian memory kernels), \(f_i\) are fermionic annihilation operators. The Feynman-Vernon influence functional: \( \mathcal{F}[j,j'] = \exp\left[ -\int_0^t ds \int_0^s du \, (j(s) - j'(s)) ( \Delta(s-u) j(u) - \Delta^*(s-u) j'(u) ) \right] \) with spectral density \( J(\omega) = \sum_k |g_k|^2 \delta(\omega - \omega_k) \). Decoherence rate: \( \Gamma(t) = \int_0^t d\tau \, \text{Re}[\Delta(\tau)] \) — no golden ratio appears in the exact solution. | CONNECTION: None found. The exact master equation y Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com