Long-time tail problem and anomalous transport in three-dimensional nonlinear lattices

Abstract

Equilibrium autocorrelation functions of heat flux in a model of three-dimensional insulating solids are investigated through nonequilibrium particle dynamics simulations. We employ the Fermi-Pasta-Ulam(FPU)-β nonlinear lattice in which there exist only nearest neighbor interactions with harmonic and bi-quadratic nonlinear terms. In an fcc lattice of the size of 1923, power-law decay of the equilibrium autocorrelation function, which is often referred to as a long-time tail, is confirmed, but its decay exponent has turned out to be 0.74(1) which is different from 1.5 expected from hydrodynamic phenomenology for three dimensional systems. This value, 0.74(1), of a decay exponent implies that thermal conductivity of this system diverges with size. Finite size effects are studied using one-dimensional FPU-β lattices.