Ballistic transport
= Ballistic transport
{title2=$\operatorname{Var}X(t)\propto t^2$}
A trajectory with a persistent random velocity $V$ has $X(t)-X(0)=Vt$. An ensemble with finite velocity variance therefore has displacement variance $t^2\operatorname{Var}V$, contrasting with the linear-in-time variance of <diffusion>. In an <impulsively kicked sinusoidal shear dispersion> model with zero transverse diffusivity, the shear phase never changes and repeated identical kicks have this ballistic scaling. Transverse diffusion instead decorrelates the velocity and permits a long-time diffusive limit.