The Role of Chaos in One-Dimensional Heat Conductivity

TL;DR

This study examines how chaos influences heat conduction in a quasi-1D gas model, revealing that strong chaos leads to size-independent conductivity and linking diffusion behavior to heat transfer properties.

Contribution

It demonstrates the impact of chaos on heat conductivity and diffusion in a quasi-1D system, providing numerical and analytical insights into temperature profiles and superdiffusion effects.

Findings

Heat conductivity becomes size-independent with strong chaos.

Diffusion and heat conduction exponents satisfy the relation =2-2/.

Superdiffusion significantly affects temperature jumps and finite-size effects.

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 $\kappa$ 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 $\alpha$ of heat conduction and diffusion exponent $\beta$ are in consistent with the formula $\alpha=2-2/\beta$. 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 $\beta$ remarkably.