Role of chaos in one-dimensional heat conductivity

We investigate the heat conduction in a quasi-one-dimensional gas model with various degrees 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 nonchaotic channels are also studied. The numerical results of divergent exponent alpha of heat conduction and diffusion exponent beta are 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 nonchaotic and chaotic cases, and for the latter case of superdiffusion the finite size affects the value of beta remarkably.