Resonant-pair energy return beyond the early Green-Kubo plateau in a quartic chain

Distinguishing rapid local energy exchange from sustained transport matters when thermal conductivity is inferred from finite simulations. In a weakly coupled chain of separable quartic oscillators, we identify a quantitative mechanism that changes an early Green–Kubo plateau: resonant neighbors exchange energy and coherently return it. The pair heat-current integral maps to the classical pendulum trapping response. Quartic homogeneity gives an energy-independent reference period $T_{\mathrm{l}\mathrm{i}\mathrm{b}}=7.77{\epsilon }^{-1\mathrm{/}2}$, where $\epsilon$ is the coupling. Without fitted parameters, the leading response predicts a negative first minimum at $0.952T_{\mathrm{l}\mathrm{i}\mathrm{b}}$ with depth $-0.74$ times the independent-cell exchange coefficient. Isolated-pair simulations test this reference and resolve finite-coupling corrections. The chain reaches its first minimum on the same time scale, with a shallower minimum and a small later residual. Comparisons with chaotic cells and energy-conserving noise show regimes in which coherent return is absent or interrupted over the measured windows. These finite-time results provide a quantitative reference for separating the early exchange plateau from subsequent correlated dynamics.