Long-time tail of the velocity autocorrelation function in a two-dimensional moderately dense hard-disk fluid

Alder and Wainwright discovered the slow power decay ~t(-d/2) (d is dimension) of the velocity autocorrelation function in moderately dense hard-sphere fluids using the event-driven molecular dynamics simulations. In the two-dimensional (2D) case, the diffusion coefficient derived using the time correlation expression in linear response theory shows logarithmic divergence, which is called the "2D long-time-tail problem." We reexamined this problem to perform a large-scale, long-time simulation with 1x10(6) hard disks using a modern efficient algorithm and found that the decay of the long tail in moderately dense fluids is slightly faster than the power decay (~1/t) . We also compared our numerical data with the prediction of the self-consistent mode-coupling theory in the long-time limit [~1/(t sqrt[ln t])] .