  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.
