Role of the range of the interactions in thermal conduction

TL;DR

This study explores how the range of interactions in a one-dimensional lattice of classical inertial rotators affects thermal conduction, revealing that Fourier's law applies only for sufficiently short-range interactions.

Contribution

It demonstrates the critical interaction range beyond which Fourier's law breaks down in a classical rotator lattice with long-range attractive couplings.

Findings

Fourier's law holds only for interactions with $ ext{α} > ext{α}_c(T)$.

Long-range interactions with $ ext{α} < ext{α}_c(T)$ lead to insulator-like behavior.

The temperature profile and energy transport depend on the interaction range.

Abstract

We investigate thermal transport along a one-dimensional lattice of classical inertial rotators, with attractive couplings which decrease with distance as $r^{-\alpha}$ ($\alpha \ge 0$), subject at its ends to Brownian heat reservoirs at different temperatures with average value $T$. By means of numerical integration of the equations of motion, we show the effects of the range of the interactions in the temperature profile and energy transport, and determine the domain of validity of Fourier's law in this context. We find that Fourier's law, as signaled by a finite $\kappa$ in the thermodynamic limit, holds only for sufficiently short range interactions, with $\alpha >\alpha_c(T)$. For $\alpha<\alpha_c(T)$, a kind of insulator behavior emerges at any $T$.