Figure 9: Simulated diffusivity and kurtosis on a one-dimensional short-ranged disorder line along with theoretical predictions Eqs. (13) and (17)–(18). diffusivity and kurtosis reveal that the long-time limit starts at t ~ τ_r and t ~ 4τ_r respectively.

a) Simulated diffusivity with respect to t/τ_r approaches its tortuosity value D_∞. Inset: Normalized diffusivity along with the theory (dashed line) given by Eqs. (13) and (17)–(18). b)Similarly, the simulated kurtosis with respect to t/τ_r approaches zero at long times but shows a non-monotonic behavior at t ≲ τ_r. Inset: Short-time limit of diffusion kurtosisshows an initial increase and a plateau at t ≲ τ_r before reaching the long-time limit for t > τ_r agreeing with the theory (dashed line) given by Eqs. (13) and (17)–(18). c)Simulated diffusivity and kurtosis (solid lines) plotted with respect to $\sqrt{{\tau }_r/t}$ approach a straight line for t ≫ τ_r where the long-time limit empirically starts. The two-fold difference in the coefficients c_K and c_D/D_∞ from Eq. (13) is apparent in the two-fold difference in the slopes of the simulated quantities for t ≫ τ_r.