Effect of bias in a reaction diffusion system in two dimensions

Abstract

We consider a single species reaction diffusion system on a two dimensional lattice where the particles $A$ are biased to move towards their nearest neighbours and annihilate as they meet; $A+A\to \varnothing$. Allowing the bias to take both negative and positive values parametrically, any nonzero bias is seen to drastically affect the behaviour of the system compared to the unbiased (simple diffusive) case. For positive bias, a finite number of dimers, which are isolated pairs of particles occurring as nearest neighbours, exist while for negative bias, a finite density of particles survive. Both the quantities vanish in a power law manner close to the diffusive limit with different exponents. In addition, a discontinuity is observed at the fully positive bias limit. The persistence behaviour is also analysed for the system.

arXiv comment8 pages, 13 figures

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• Tagged particle dynamics in one dimensional $A+A\to kA$ models with the particles biased to diffuse towards their nearest neighbour
• $A+A\to \varnothing$ system in one dimension with particle motion determined by nearest neighbour distances: results for parallel updates