Thermal conductance of the Fermi-Pasta-Ulam chains: Atomic to mesoscopic transition

TL;DR

This paper investigates how thermal conductance in FPU chains transitions from atomic to mesoscopic scales, revealing a significant deviation at atomic scales due to contact resistance and establishing a temperature scaling law.

Contribution

It demonstrates the deviation of thermal conductance at atomic scales from mesoscopic behavior and connects these regimes across various nonlinear FPU-like models.

Findings

Atomic chains follow a log-log scaling with temperature, with a coefficient twice that of mesoscopic systems.

The transition from atomic to mesoscopic conductance is smooth and applicable to other nonlinear models.

Results are relevant for nanoscale thermal management and device design.

Abstract

We demonstrate that in the atomic-scale limit the thermal conductance $\mathcal K$ of the FPU model and its variants strongly deviates from the mesoscopic behavior due to the relevance of contact resistance. As a result, atomic chains follow $\log \mathcal K = \nu \log T$, where the power law coefficient $\nu$ is exactly two times larger than the mesoscopic value. We smoothly interconnect the atomic and mesoscopic limits, and demonstrate that this turnover behavior takes place in other nonlinear FPU-like models. Our results are significant for nanoscale applications, manifesting an atomic thermal conductance with temperature scaling superior to the mesoscopic limit.