Simulational Study on Dimensionality-Dependence of Heat Conduction

Abstract

Heat conduction phenomena are studied theoretically using computer simulation. The systems are crystal with nonlinear interaction, and fluid of hard-core particles. Quasi-one-dimensional system of the size of $L_x\times L_y\times L_z(L_z\gg L_x,L_y)$ is simulated. Heat baths are put in both end: one has higher temperature than the other. In the crystal case, the interaction potential $V$ has fourth-order non-linear term in addition to the harmonic term, and Nose-Hoover method is used for the heat baths. In the fluid case, stochastic boundary condition is charged, which works as the heat baths. Fourier-type heat conduction is reproduced both in crystal and fluid models in three-dimensional system, but it is not observed in lower dimensional system. Autocorrelation function of heat flux is also observed and long-time tails of the form of $\sim t^{-d/2}$, where $d$ denotes the dimensionality of the system, are confirmed.

4 pages including 3 figures

References in corpus (1)

• Heat conduction in the diatomic Toda lattice revisited

Cited by in corpus (11)

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• Anomalous energy transport in FPU-$\beta$ chain
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• Divergent Thermal Conductivity in Three-dimensional Nonlinear lattices
• Nonequilibrium Microscopic Distribution of Thermal Current in Particle Systems
• Nonequilibrium Molecular Dynamics Simulation of Interacting Many Electrons Scattered by Lattice Vibrations
• Distribution of Microscopic Energy Flux in Equilibrium State