Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map

TL;DR

This paper investigates how the thermal conductivity of a 1D coupled rotator lattice varies with temperature, clarifying previous conflicting results and supporting the absence of a phase transition, while drawing parallels with the standard map.

Contribution

The study provides a new power law description of temperature dependence in the coupled rotator lattice and resolves previous discrepancies regarding its thermal behavior.

Findings

Thermal conductivity follows a power law with temperature.

No phase transition occurs in the 1D coupled rotator lattice.

Diffusion behavior resembles that of the standard map.

Abstract

In contrary to other 1D momentum-conserving lattices such as the Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) lattice, the 1D coupled rotator lattice is a notable exception which conserves total momentum while exhibits normal heat conduction behavior. The temperature behavior of the thermal conductivities of 1D coupled rotator lattice had been studied in previous works trying to reveal the underlying physical mechanism for normal heat conduction. However, two different temperature behaviors of thermal conductivities have been claimed for the same coupled rotator lattice. These different temperature behaviors also intrigue the debate whether there is a phase transition of thermal conductivities as the function of temperature. In this work, we will revisit the temperature dependent thermal conductivities for the 1D coupled rotator lattice. We find that the temperature dependence follows a power law behavior which is different with the previously found temperature behaviors. Our results also support the claim that there is no phase transition for 1D coupled rotator lattice. We also give some discussion about the similarity of diffusion behaviors between the 1D coupled rotator lattice and the single kicked rotator also called the Chirikov standard map.