From three-dimensional linearized hydrodynamic equations, it is found that the heat conductivity is proportional to $(L_x/(L_y^2 L_z^2))^{ 1/3}$, 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.
Categories: cond-mat.stat-mech