Validity of Fourier's law in one-dimensional momentum-conserving lattices with asymmetric interparticle interactions

TL;DR

This study investigates heat conduction in one-dimensional momentum-conserving lattices with asymmetric interactions, revealing finite-size effects that mimic Fourier's law but ultimately confirm divergence in the thermodynamic limit.

Contribution

It provides numerical evidence that heat conductivity diverges as lattice size increases, confirming theoretical predictions for asymmetric momentum-conserving lattices.

Findings

Finite-size effects cause apparent Fourier-like behavior

Heat conductivity diverges with increasing lattice length

Results support existing theories of divergence in the thermodynamic limit

Abstract

We have numerically studied heat conduction in a few one-dimensional momentum-conserving lattices with asymmetric interparticle interactions by the nonequilibrium heat bath method, the equilibrium Green-Kubo method, and the heat current power spectra analysis. Very strong finite-size effects are clearly observed. Such effects make the heat conduction obey a Fourier-like law in a wide range of lattice lengths. However, in yet longer lattice lengths, the heat conductivity regains its power-law divergence. Therefore the power-law divergence of the heat conductivity in the thermodynamic limit is verified, as is expected by many existing theories.