$A+A \rightarrow \emptyset $ model with a bias towards nearest neighbor

TL;DR

This study investigates how a local bias towards nearest neighbors in a reaction-diffusion model alters its universality class, changing the dynamic exponent from 2 to 1, with analytical and simulation comparisons.

Contribution

It introduces a biased A+A reaction model on a ring, demonstrating a shift in universality class due to local bias, supported by analytical and simulation analysis.

Findings

The dynamic exponent z changes from 2 to 1 with any non-zero bias.

The distribution of spacings follows a scaling form with different behaviors in analytical and simulation approaches.

The bias influences the universality class despite being a local, time-space specific effect.

Abstract

We have studied $A+A \rightarrow \emptyset$ reaction-diffusion model on a ring, with a bias $\epsilon$ $(0 \leq \epsilon \leq 0.5)$ of the random walkers $A$ to hop towards their nearest neighbor. Though the bias is local in space and time, we show that it alters the universality class of the problem. The $z$ exponent, which describes the growth of average spacings between the walkers with time, changes from the value 2 at $\epsilon=0$ to the mean-field value of unity for any non-zero $\epsilon$. We study the problem analytically using independent interval approximation and compare the scaling results with that obtained from simulation. The distribution $P(k,t)$ of the spacing $k$ between two walkers (per site) is given by $t^{-2/z} f(k/t^{1/z})$ as expected; however, the scaling function shows different behaviour in the two approaches.