Self-diffusion in a two-dimensional simple fluid is investigated by both
analytical and numerical means. We investigate the anomalous aspects of
self-diffusion in two-dimensional fluids with regards to the mean square
displacement, the time-dependent diffusion coefficient, and the velocity
autocorrelation function using a consistency equation relating these
quantities. We numerically confirm the consistency equation by extensive
molecular dynamics simulations for finite systems, corroborate earlier results
indicating that the kinematic viscosity approaches a finite, non-vanishing
value in the thermodynamic limit, and establish the finite size behavior of the
diffusion coefficient. We obtain the exact solution of the consistency equation
in the thermodynamic limit and use this solution to determine the large time
asymptotics of the mean square displacement, the diffusion coefficient, and the
velocity autocorrelation function. An asymptotic decay law of the velocity
autocorrelation function resembles the previously known self-consistent form,
1/(tlnt), however with a rescaled time.Comment: 10 pages, to appear in New Journal of Physic