Divergent Thermal Conductivity in Three-dimensional Nonlinear lattices

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.

4 pages, 5 figures. Accepted for publication in J. Phys. Soc. Japan Letters

References in corpus (3)

• Thermal conduction in classical low-dimensional lattices
• Anomalous heat conduction in one dimensional momentum-conserving systems
• Studies of thermal conductivity in Fermi-Pasta-Ulam like lattices

Cited by in corpus (4)

• Anomalous Heat Conduction in Three-Dimensional Nonlinear Lattices
• Long-Time Behavior of Velocity Autocorrelation Function for Interacting Particles in a Two-Dimensional Disordered System
• Thermal rectification in three-dimensional mass-graded anharmonic oscillator lattices
• Distribution of Microscopic Energy Flux in Equilibrium State