Large-Scale Simulations of Diffusion-Limited n-Species Annihilation

We present results from computer simulations for diffusion-limited \(n\)-species annihilation, \(A_i+A_j\to0\) \((i,j=1,2,...,n;i\neq j)\), on the line, for lattices of up to \(2^{28}\) sites, and where the process proceeds to completion (no further reactions possible), involving up to \(10^{15}\) time steps. These enormous simulations are made possible by the renormalized reaction-cell method (RRC). Our results suggest that the concentration decay exponent for \(n\) species is \(\a(n)=(n-1)/2n\) instead of \((2n-3)/(4n-4)\), as previously believed, and are in agreement with recent theoretical arguments \cite{tauber}. We also propose a scaling relation for \(\Delta\), the correction-to-scaling exponent for the concentration decay; \(c(t)\sim t^{-\a}(A+Bt^{-\Delta})\).