Crossover from Fermi-Pasta-Ulam to normal diffusive behaviour in heat conduction through open anharmonic lattices

TL;DR

This study investigates heat conduction in anharmonic lattices with double-well potentials across different dimensions, revealing a crossover from Fermi-Pasta-Ulam-like behavior at high temperatures to normal diffusive conduction at low temperatures.

Contribution

It demonstrates the temperature-dependent transition in heat conduction behavior in anharmonic lattices with double-well potentials across multiple dimensions.

Findings

High-temperature regime shows FPU-like length dependence of heat current.

Low-temperature regime exhibits Fourier's law with diffusive heat conduction.

Behavior transition observed consistently in 1D, 2D, and 3D lattices.

Abstract

We study heat conduction in one, two and three dimensional anharmonic lattices connected to stochastic Langevin heat baths. The inter-atomic potential of the lattices is double-well type, i.e., $V_{\rm DW}(x)=k_2x^2/2+k_4 x^4/4$ with $k_2<0$ and $k_4>0$. We observe two different temperature regimes of transport: a high-temperature regime where asymptotic length dependence of nonequilibrium steady state heat current is similar to the well-known Fermi-Pasta-Ulam lattices with an inter-atomic potential, $V_{\rm FPU}(x)=k_2x^2/2+k_4 x^4/4$ with $k_2,k_4>0$. A low temperature regime where heat conduction is diffusive normal satisfying Fourier's law. We present our simulation results at different temperature regimes in all dimensions.