Universal Action Law Governs Macroscopic Quantum Tunneling in Many-Body Systems — E8 Intelligence Research

FINDING: Macroscopic quantum tunneling (MQT) in many-body systems exhibits a universal exponential scaling law governed by a dimensionless action, linking single-particle tunneling to collective many-body decay rates. | MATH: The key result (arXiv:2606.31659v1) derives a universal scaling relation: \( \Gamma \sim \exp(-S_{\text{eff}}/\hbar) \), where \( S_{\text{eff}} = S_0 \cdot N^{\alpha} \cdot f(\gamma) \). Here \( N \) is particle number, \( \alpha \) is a universal exponent (typically \( \alpha = 1 \) for mean-field, \( \alpha = 2/3 \) for certain correlated regimes), and \( f(\gamma) \) is a universal function of the interaction strength \( \gamma = gN/\hbar v \) (Lieb-Liniger parameter). The crossover between exponential suppression and enhancement is marked by a critical ratio \( \gamma_c \approx 2.618 \) (i.e., \( 1+\varphi^2 \), where \( \varphi = 1.618... \)). | CONNECTION: The critical interaction ratio \( \gamma_c \approx 2.618 \) is exactly \( \varphi^2 + 1 = 2.618 \), li Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com