Feynman-Vernon Influence Functional for Moving Thermal Environments: A Review — E8 Intelligence Research

FINDING: The search results are dominated by pedagogical videos and one relevant arXiv paper on the Feynman-Vernon influence functional for a moving thermal environment; no exact decoherence-rate temperature formula is extracted from the raw results. | MATH: The arXiv paper (1803.10300) formalizes the Feynman-Vernon influence functional \( \mathcal{F}[x,x'] = \exp\left\{-\frac{1}{\hbar}\int_0^t\int_0^t [x(s)-x'(s)] K(s-s') [x(s')-x'(s')] ds\,ds'\right\} \), with kernel \( K(\tau) = \int_0^\infty \frac{J(\omega)}{\pi} \left[ \coth\left(\frac{\hbar\omega}{2k_B T}\right)\cos(\omega\tau) - i\sin(\omega\tau) \right] d\omega \), where \( J(\omega) \) is the spectral density. The temperature dependence enters via the hyperbolic cotangent \( \coth(\hbar\omega/2k_BT) \), which in the high-T limit gives \( 2k_BT/\hbar\omega \) (linear in T), and in the low-T limit gives 1 (temperature-independent zero-point fluctuations). | CONNECTION: The kernel's structure contains the Matsubara frequencies \( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com