Segregation in diffusion-limited multispecies pair annihilation

TL;DR

This paper investigates the long-time behavior and segregation phenomena in multispecies pair annihilation reactions across different dimensions, revealing how particle density decay rates depend on the number of species and spatial dimension.

Contribution

It provides analytical and simulation-based insights into how segregation and decay rates vary with species number and dimension in multispecies annihilation reactions.

Findings

In 1D, the system segregates into single-species domains with species-dependent decay exponents.

Derived an explicit formula for the decay exponent alpha(q) in 1D.

In higher dimensions, segregation occurs only for fewer species, with universal decay for larger q.

Abstract

The kinetics of the q species pair annihilation reaction (A_i + A_j -> 0 for 1 <= i < j <= q) in d dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time regime the total particle density decays as rho(t) ~ t^{- alpha}. For d = 1 the system segregates into single species domains, yielding a different value of alpha for each q; for a simplified version of the model in one dimension we derive alpha(q) = (q-1) / (2q). Within mean-field theory, applicable in d >= 2, segregation occurs only for q < 1 + (4/d). The only physical realisation of this scenario is the two-species process (q = 2) in d = 2 and d = 3, governed by an extra local conservation law. For d >= 2 and q >= 1 + (4/d) the system remains disordered and its density is shown to decay universally with the mean-field power law (alpha = 1) that also characterises the single-species annihilation process A + A -> 0.