Multi-species pair annihilation reactions

TL;DR

This paper investigates diffusion-limited multi-species pair annihilation reactions, revealing that in higher dimensions the decay resembles single-species reactions, while in one dimension segregation leads to a q-dependent decay law, supported by simulations.

Contribution

It demonstrates that for q > 2 and d >= 2, the asymptotic decay matches single-species behavior, and derives an exact q-dependent decay exponent in one dimension.

Findings

In higher dimensions, decay is similar to single-species annihilation.

In one dimension, segregation causes a q-dependent power-law decay.

Monte Carlo simulations support the theoretical results.

Abstract

We consider diffusion-limited reactions A_i + A_j -> 0 (1 <= i < j <= q) in d space dimensions. For q > 2 and d >= 2 we argue that the asymptotic density decay for such mutual annihilation processes with equal rates and initial densities is the same as for single-species pair annihilation A + A -> 0. In d = 1, however, particle segregation occurs for all q < oo. The total density decays according to a $q$ dependent power law, rho(t) ~ t^{-\alpha(q)}. Within a simplified version of the model \alpha(q) = (q-1) / 2q can be determined exactly. Our findings are supported through Monte Carlo simulations.