  We investigate Fickian diffusion in two-dimensional (2D) Yukawa liquids using
molecular dynamics simulations. We compute the self-van Hove correlation
function $G_s(r,t)$, and the self-intermediate scattering function $F_s(k,t)$
and compare these functions with those obtained from mean-squared displacement
MSD using the Gaussian approximation. According to this approximation, a linear
MSD with time implies a Gaussian behavior for $G_s(r,t)$ and $F_s(k,t)$ at all
times. Surprisingly, we find that these functions deviate from Gaussian at
intermediate time scales, indicating the failure of the Gaussian approximation.
Furthermore, we quantify these deviations by the non-Gaussian parameter, and we
find that the deviations increase with decreasing the temperature of the
liquid. The origin of the non-Gaussian behavior may be the heterogeneous
dynamics of dust particles observed in 2D Yukawa liquids.
