论文标题
在两个物种排除过程中的聚类和有限尺寸效应
Clustering and finite size effects in a two-species exclusion process
论文作者
论文摘要
我们研究了两个物种排除过程的颗粒的簇尺寸分布，该过程涉及两个相对指向物种的完全不对称的传输过程，并在一维晶格上具有随机方向转换。作为$ q $的函数 - 粒子的翻译速率和方向开关速率的比率，在$ q \ rightarrow 0 $中，群集大小的概率分布是群集大小$ m $的指数衰减功能，并且与tasep的群集大小分布完全相似。对于$ q >> 1 $，可以将模型映射到持久的排除过程（PEP）和平均群集大小，$ \ langle m \ rangle \ propto q^{1/2} $。我们在此限制下获得平均簇大小的近似表达式。对于$ l $晶格站点的有限系统尺寸系统，对于粒子数密度$ρ$，群集尺寸的概率分布显示出独特的峰值，这对应于单个大小$ M_S =ρl$的单个群集的形成。但是，这个峰在热力学极限$ l \ rightarrow \ infty $中消失。有趣的是，此最大尺寸群集的概率，$ p（m_s）$，表现出缩放行为，因此，就缩放变量而言，$ q_1 \ equiv q/l^2ρ（1-ρ）$，对于此群集的概率，观察到数据崩溃。与此最小模型观察到的聚类相关的统计特征也可能与理解{\ it Active}粒子系统中的群集特性中的聚类特性有关。
We study the cluster size distribution of particles for a two-species exclusion process which involves totally asymmetric transport process of two oppositely directed species with stochastic directional switching of the species on a 1D lattice. As a function of $Q$ - the ratio of the translation rate and directional switching rate of particles, in the limit of $Q \rightarrow 0$, the probability distribution of the cluster size is an exponentially decaying function of cluster size $m$ and is exactly similar to the cluster size distribution of a TASEP. For $Q>>1$, the model can be mapped to persistent exclusion process (PEP) and the average cluster size, $\langle m \rangle \propto Q^{1/2} $. We obtain an approximate expression for the average cluster size in this limit. For finite system size system of $L$ lattice sites, for a particle number density $ρ$, the probability distribution of cluster sizes exhibits a distinct peak which corresponds to the formation of a single cluster of size $m_s = ρL$. However this peak vanishes in the thermodynamic limit $ L \rightarrow \infty$. Interestingly, the probability of this largest size cluster, $P(m_s)$, exhibits scaling behaviour such that in terms of scaled variable $Q_1 \equiv Q/L^2 ρ(1-ρ)$, data collapse is observed for the probability of this cluster. The statistical features related to clustering observed for this minimal model may also be relevant for understanding clustering characteristics in {\it active } particles systems in confined 1D geometry.
