Divergent Thermal Conductivity in Three-dimensional Nonlinear lattices

Details Divergent Thermal Conductivity in Three-dimensional Nonlinear lattices Divergent Thermal Conductivity in Three-dimensional Nonlinear lattices

2006-08-07

arxiv.org/abs/cond-mat/0608152v2

J. Phys. Soc. Jpn. 75, 103001 (2006)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1143/JPSJ.75.103001

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.

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