  The bare diffusion coefficient is given as the time integral of the peculiar
velocity autocorrelation function or PVACF and this result is different from
the well known Green-Kubo formula. The bare diffusion coefficient characterizes
the diffusion process on a length scale lambda. The PVACF is given here for the
first time in terms of the positions and velocities of the N particles of the
system so the PVACF is in a form suitable for evaluation by molecular dynamics
simulations. The computer simulations show that for the two dimensional hard
disk system, the PVACF decays increasingly rapidly in time as lambda is reduced
and this is probably a general characteristic.
