Heat conduction in 1D lattices with on-site potential

TL;DR

This paper investigates heat conduction in 1D lattices with on-site potentials through numerical simulations, revealing that anharmonicity alone does not ensure normal heat conductivity, which depends on nonlinear excitations and their interactions.

Contribution

It demonstrates that the type of nonlinear excitations and their interactions determine heat conduction, challenging previous assumptions that anharmonicity alone suffices.

Findings

Heat conduction depends on the spectrum of nonlinear excitations.

Different models exhibit distinct scattering mechanisms.

Temperature influences the dominant scattering processes.

Abstract

The process of heat conduction in one-dimensional lattice with on-site potential is studied by means of numerical simulation. Using discrete Frenkel-Kontorova, $\phi$--4 and sinh-Gordon we demonstrate that contrary to previously expressed opinions the sole anharmonicity of the on-site potential is insufficient to ensure the normal heat conductivity in these systems. The character of the heat conduction is determined by the spectrum of nonlinear excitations peculiar for every given model and therefore depends on the concrete potential shape and temperature of the lattice. The reason is that the peculiarities of the nonlinear excitations and their interactions prescribe the energy scattering mechanism in each model. For models sin-Gordon and $\phi$--4 phonons are scattered at thermalized lattice of topological solitons; for sinh-Gordon and $\phi$--4 - models the phonons are scattered at localized high-frequency breathers (in the case of $\phi$--4 the scattering mechanism switches with the growth of the temperature).