Divergent Thermal Conductivity in Three-dimensional Nonlinear lattices

TL;DR

This study uses particle dynamics simulations to explore heat conduction in 3D nonlinear lattices, revealing divergent thermal conductivity and slow energy flux decay, which differ from traditional models.

Contribution

It demonstrates divergent thermal conductivity in 3D nonlinear lattices with a specific potential, showing slower decay of energy flux autocorrelation than conventional systems.

Findings

Logarithmic divergence of energy flux with system size

Power-law decay of energy flux autocorrelation (~t^{-1})

Similar behavior observed in four-dimensional systems

Abstract

Heat conduction in three-dimensional nonlinear lattices is investigated using a particle dynamics simulation. The system is a simple three-dimensional extension of the Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) nonlinear lattices, in which the interparticle potential has a biquadratic term together with a harmonic term. The system size is $L\times L\times 2L$, and the heat is made to flow in the $2L$ direction the Nose-Hoover method. Although a linear temperature profile is realized, the ratio of enerfy flux to temperature gradient shows logarithmic divergence with $L$. The autocorrelation function of energy flux $C(t)$ is observed to show power-law decay as $t^{-0.98\pm 0,25}$, which is slower than the decay in conventional momentum-cnserving three-dimensional systems ($t^{-3/2}$). Similar behavior is also observed in the four dimensional system.