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The Role of Chaos in One-Dimensional Heat Conductivity

Jun-Wen Mao·You-Quan Li·Yong-Yun Ji
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Abstract

We investigate the heat conduction in a quasi 1-D gas model with various degree of chaos. Our calculations indicate that the heat conductivity $κ$ is independent of system size when the chaos of the channel is strong enough. The different diffusion behaviors for the cases of chaotic and non-chaotic channels are also studied. The numerical results of divergent exponent $α$ of heat conduction and diffusion exponent $β$ are in consistent with the formula $α=2-2/β$. We explore the temperature profiles numerically and analytically, which show that the temperature jump is primarily attributed to superdiffusion for both non-chaotic and chaotic cases, and for the latter case of superdiffusion the finite-size affects the value of $β$ remarkably.

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Jun-Wen Mao, You-Quan Li, Yong-Yun Ji. 2004-12-07. The Role of Chaos in One-Dimensional Heat Conductivity. https://doi.org/10.1103/physreve.71.061202

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