Anomalous Heat Conduction in Quasi-One-Dimensional Gases

TL;DR

This paper derives a size-dependent formula for heat conductivity in quasi-one-dimensional gases from hydrodynamic equations, confirming the theoretical prediction with molecular dynamics simulations.

Contribution

It introduces a new size dependence of heat conductivity in quasi-one-dimensional gases and verifies it through molecular dynamics simulations.

Findings

Heat conductivity scales as $(L_x/(L_y^2 L_z^2))^{1/3}$.

Size dependence confirmed by molecular dynamics.

Critical condition for size dependence derived as $ ightarrow ext{L}_x/(n^{1/2} ext{L}_y^{5/4} ext{L}_z^{5/4}) ightarrow ext{large}$.

Abstract

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.