Resonant-pair energy return beyond the early Green-Kubo plateau in a quartic chain
Abstract
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 Tlib=7.77ε−1/2, where ε is the coupling. Without fitted parameters, the leading response predicts a negative first minimum at 0.952Tlib 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.
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BibTeX
@misc{olszewski2026resonantpair,
title = {{Resonant-pair energy return beyond the early Green-Kubo plateau in a quartic chain}},
author = {Julian Olszewski and Zijian Liu and Jie Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30172},
eprint = {2610.30172},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30172},
}
RIS
TY - UNPB
TI - Resonant-pair energy return beyond the early Green-Kubo plateau in a quartic chain
AU - Julian Olszewski
AU - Zijian Liu
AU - Jie Xu
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.30172
UR - https://arxiv.org/abs/2610.30172
AB - 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_lib=7.77ε^−1/2, where ε is the coupling. Without fitted parameters, the leading response predicts a negative first minimum at 0.952T_lib 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.
ER -