Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs

TL;DR

This paper studies heat transport in long-range interacting oscillator chains coupled to thermal reservoirs, revealing different regimes of energy transfer dominated by direct coupling or diffusive processes depending on the decay exponent.

Contribution

It introduces a decomposition of heat current accounting for direct transfer and diffusion, highlighting how long-range interactions influence thermal transport regimes.

Findings

For 0 ≤ α < 1, direct transfer dominates heat flow.

Heat current becomes independent of system size when thermalized regions scale with N.

For α > 1, heat transport is mainly diffusive, with normal or anomalous behavior depending on the system.

Abstract

We investigate thermal conduction in arrays of long-range interacting rotors and Fermi-Pasta-Ulam (FPU) oscillators coupled to two reservoirs at different temperatures. The strength of the interaction between two lattice sites decays as a power $\alpha$ of the inverse of their distance. We point out the necessity of distinguishing between energy flows towards/from the reservoirs and those within the system. We show that energy flow between the reservoirs occurs via a direct transfer induced by long-range couplings and a diffusive process through the chain. To this aim, we introduce a decomposition of the steady-state heat current that explicitly accounts for such direct transfer of energy between the reservoir. For $0\leq \alpha<1$, the direct transfer term dominates, meaning that the system can be effectively described as a set of oscillators each interacting with the thermal baths. Also, the heat current exchanged with the reservoirs depends on the size of the thermalised regions: in the case in which such size is proportional to the system size $N$, the stationary current is independent on $N$. For $\alpha > 1$, heat transport mostly occurs through diffusion along the chain: for the rotors transport is normal, while for FPU the data are compatible with an anomalous diffusion, possibly with an $\alpha$ -dependent characteristic exponent.