Anomalous Heat Conduction in Quasi-One-Dimensional Gases

From three-dimensional linearized hydrodynamic equations, it is found that the heat conductivity is proportional to $(L_x\mathrm{/}(L_y^2{L}_z^2){)}^{1\mathrm{/}3}$, where $L_x$, $L_y$ and $L_z$ are the lengths of the system along the $x$, $y$ and $z$ directions, and we consider the case in which $L_x\gg L_y,L_z$. The necessary condition for such a size dependence is derived as $\phi \equiv L_x/(n^{1/2} L_y^{5/4} L_z^{5/4}) \gg 1$,where$\phi$ is the critical condition parameter and $n$ is the number density. This size dependence of the heat conductivity has been confirmed by molecular dynamics simulation.