# Eliminating the cuspidal temperature profile of a non-equilibrium chain

## TL;DR

This paper investigates how pinning interactions influence the temperature profile in a non-equilibrium chain model, demonstrating that appropriate pinning can eliminate cuspidal temperature profiles and induce temperature plateaux.

## Contribution

The study reveals that introducing and tuning pinning interactions can remove cuspidal temperature profiles and produce stable temperature plateaux in the RLL model.

## Key findings

- Proper pinning values can switch the temperature profile from cuspidal to monotonic.
- Temperature plateaux emerge at specific pinning thresholds.
- Heat flux cumulants reach maxima at the first threshold, indicating a 'phonon box' behavior.

## Abstract

In 1967, Z. Rieder, J. L. Lebowitz and E. Lieb (RLL) introduced a model of heat conduction on a crystal that became a milestone problem of non-equilibrium statistical mechanics. Along with its inability to reproduce Fourier's Law - which subsequent generalizations have been trying to amend - the RLL model is also characterized by awkward cusps at the ends of the non-equilibrium chain, an effect that has endured all these years without a satisfactory answer. In this paper, we first show that such trait stems from the insufficiency of pinning interactions between the chain and the substrate. Assuming the possibility of pinning the chain, the analysis of the temperature profile in the space of parameters reveals that for a proper combination of the border and bulk pinning values, the temperature profile may shift twice between the RLL cuspidal behavior and the expected monotonic local temperature evolution along the system, as a function of the pinning. At those inversions, the temperature profile along the chain is characterized by perfect plateaux: at the first threshold, the cumulants of the heat flux reach their maxima and the vanishing of the two-point velocity correlation function for all sites of the chain so that the system behaves similarly to a "phonon box". On the other hand, at the second change of the temperature profile, we still have the vanishing of the two-point correlation function but only for the bulk, which explains the emergence of the temperature plateau and thwarts the reaching of the maximal values of the cumulants of the heat flux.