Heat conduction and diffusion of hard disks in a narrow channel

Using molecular dynamics we study heat conduction and diffusion of hard disks in one dimensional narrow channels. When collisions preserve momentum the heat conduction $\kappa$ diverges with the number of disks $N$ as $\kappa\sim N^\alpha$ $(\alpha \approx 1/3)$. Such a behaviour is seen both when the ordering of disks is fixed ('pen-case' model), and when they can exchange their positions. Momentum conservation results also in sound-wave effects that enhance diffusive behaviour and on an intermediate time scale (that diverges in the thermodynamic limit) normal diffusion takes place even in the 'pen-case' model. When collisions do not preserve momentum, $\kappa$ remains finite and sound-wave effects are absent.