论文标题
$ a+ a \ to \ emptySet $ y反应具有动态偏见的粒子，以在一个维度上远离其最近的邻居
$A+ A \to \emptyset$ reaction for particles with a dynamic bias to move away from their nearest neighbour in one dimension
论文作者
论文摘要
我们考虑在一个维度上具有动态偏置的粒子的动力学。在这里，粒子向他们最近的邻居移动，概率为$ 0.5+ε$，其中$ -0.5 \leqε<0 $。 $ε_c= -0.5 $是最近邻居交互严格排斥的确定性限制。我们表明，负面偏见会大大变化，随着时间$ t $，存活粒子$ρ（t）$和持久性概率$ p（t）$的行为。 $ρ（t）$衰减为$ a/（\ log t）^b $，其中$ b $以$ε-ε_c$增加。 $ p（t）$显示了带有非普遍衰减参数的拉伸指数衰减。标记粒子在其起源的位置$ x $处的概率$π（x，t）$被认为是所有$ε<0 $的高斯;关联的缩放变量为$ x/t^α$，其中$α$以功率法的方式接近已知限制值$ 1/4 $作为$ε\toε_c$。还研究了通过对粒子进行标记的一些其他特征。将结果与正偏见的情况进行了比较，这是一个很好的研究问题。
We consider the dynamics of particles undergoing the reaction $A+A \to \emptyset$ in one dimension with a dynamic bias. Here the particles move towards their nearest neighbour with probability $0.5+ε$ where $-0.5 \leq ε< 0$. $ε_c = -0.5$ is the deterministic limit where the nearest neighbour interaction is strictly repulsive. We show that the negative bias changes drastically the behaviour of the fraction of surviving particles $ρ(t)$ and persistence probability $P(t)$ with time $t$. $ρ(t)$ decays as $a/ (\log t)^b$ where $b$ increases with $ε- ε_c$. $P(t)$ shows a stretched exponential decay with non-universal decay parameters. The probability $Π(x,t)$ that a tagged particle is at position $x$ from its origin is found to be Gaussian for all $ε<0$; the associated scaling variable is $x/t^α$ where $α$ approaches the known limiting value $1/4$ as $ε\to ε_c$, in a power law manner. Some additional features of the dynamics by tagging the particles are also studied. The results are compared to the case of positive bias, a well studied problem.
