Diffusion-distance convention ($\ell \sim \sqrt{Dt}$)

The scale $\sqrt{Dt}$ characterizes diffusion over time $t$. For unrestricted isotropic diffusion, the rms displacement in one coordinate is $\sqrt{2Dt}$ and the total three-dimensional rms displacement is $\sqrt{6Dt}$. Stating the convention avoids spurious disagreement over a numerical prefactor.