Moving-Bath Influence Functional: Generalizing Feynman-Vernon to Non-Stationary Environments — E8 Intelligence Research

FINDING: The most substantive mathematical content is in the Feynman-Vernon model of a moving thermal environment (arXiv:1803.10300), which generalizes the influence functional to non-stationary, moving baths — the YouTube results are pedagogical noise with no derivable equations. | MATH: The Feynman-Vernon influence functional \( \mathcal{F}[x,x'] = \exp\left[-\frac{1}{\hbar}\int_{t_0}^{t} dt' \int_{t_0}^{t'} ds \, (x(t')-x'(t')) \left( \eta(t'-s) (x(s)-x'(s)) + i \nu(t'-s) (x(s)+x'(s)) \right) \right] \), where \( \eta(t) = \int_0^\infty \frac{d\omega}{\pi} J(\omega) \cos(\omega t) \) (dissipation kernel) and \( \nu(t) = \int_0^\infty \frac{d\omega}{\pi} J(\omega) \coth(\hbar\omega/2k_B T) \sin(\omega t) \) (noise kernel). For Lorentzian spectral density \( J(\omega) = \frac{2\gamma \omega_0^2 \omega}{\omega_0^2 + \omega^2} \), the decoherence rate scales as \( \Gamma \propto \gamma k_B T / \hbar \) in the high-T limit (linear in T), and as \( \Gamma \propto \gamma (k_B T/\hbar)^2 / Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com