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Alder and Wainwright discovered the slow power decay $\sim t^{-d/2}$($d$:dimension) of the velocity autocorrelation function in moderately densehard sphere fluids using the event-driven molecular dynamics simulations. Inthe two-dimensional case, the diffusion coefficient derived using the timecorrelation expression in linear response theory shows logarithmic divergence,which is called the ``2D long-time-tail problem''. We revisited this problem toperform a large-scale, long-time simulation with one million hard disks using amodern efficient algorithm and found that the decay of the long tail inmoderately dense fluids is slightly faster than the power decay ($\sim 1/t$).We also compared our numerical data with the prediction of the self-consistentmode-coupling theory in the long time limit ($\sim 1/(t\sqrt{\ln{t}})$).

Long Time Tail of the Velocity Autocorrelation Function in a Two-Dimensional Moderately Dense Hard Disk Fluid