Anomalous decay in asynchronous ballistic annihilation

Space-time snapshot of the particles.

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,
E. Ben-Naim, S. Redner, and P. L. Krapivsky, J. Phys. A 29, L561 (1996); (cond-mat/9604106).

Sidney Redner <>
Last modified: Mon Mar 26 07:33:37 EST 2001