Consider the annihilation reaction A+A--->0 in one dimension when
each particle equiprobably has a velocity +V or -V, as well as a superimposed
diffusion with diffusion coefficient D. If D=0, then the particle density
decays as t^{-1/2}. Similarly, if V=0, the particle density also
decays as t^{-1/2}. Surprisingly, when both V and D are non zero,
the particle density decays as t^{-3/4}!. Pictorially, this faster
decay stems from the fact that particles with the same velocity can meet and
react because of the diffusion. A space-time picture which illustrates both
the reactions among same-velocity and opposite-velocity particle is shown
below. More details can be found in Two Scales
in Asynchronous Ballistic Annihilation, |