论文标题
KPZ中的非组织概括性TASEP和干扰机制
Nonstationary generalized TASEP in KPZ and jamming regimes
论文作者
论文摘要
我们研究了具有广义更新的完全不对称排除过程的模型，该模型与通常的完全不对称的排除过程相比，具有附加的参数增强粒子的聚类。我们在两种类型的初始条件下得出了由颗粒在无限晶格上传播的距离的精确多颗粒分布：步骤和交替一次。研究了确切公式的两个不同尺度限制。在与Kardar-Parisi-Zhang（KPZ）普遍性相关的第一个缩放下，我们证明了缩放粒子位置与通用eiry $ _2 $和Airy $ _1 $过程的有限维分布的联合分布的融合。在第二个尺度下，我们证明了相同位置分布与两个新的随机过程的有限维分布的收敛性，这些过程描述了KPZ制度与确定性聚合方案之间的过渡，其中粒子将其粘在一起成一个单个巨型群集作为一个粒子。结果表明，过渡分布具有通风的过程，并且完全相关的高斯波动是限制情况。我们还提出了启发式论点，解释了KPZ制度中从渐近分析中出现的非宇宙缩放常数如何与无限系统中翻译不变的固定状态的性质有关，以及模型的参数应如何在过渡性方面缩放。
We study the model of the totally asymmetric exclusion process with generalized update, which compared to the usual totally asymmetric exclusion process, has an additional parameter enhancing clustering of particles. We derive the exact multiparticle distributions of distances travelled by particles on the infinite lattice for two types of initial conditions: step and alternating once. Two different scaling limits of the exact formulas are studied. Under the first scaling associated to Kardar-Parisi-Zhang (KPZ) universality class we prove convergence of joint distributions of the scaled particle positions to finite-dimensional distributions of the universal Airy$_2$ and Airy$_1$ processes. Under the second scaling we prove convergence of the same position distributions to finite-dimensional distributions of two new random processes, which describe the transition between the KPZ regime and the deterministic aggregation regime, in which the particles stick together into a single giant cluster moving as one particle. It is shown that the transitional distributions have the Airy processes and fully correlated Gaussian fluctuations as limiting cases. We also give the heuristic arguments explaining how the non-universal scaling constants appearing from the asymptotic analysis in the KPZ regime are related to the properties of translationally invariant stationary states in the infinite system and how the parameters of the model should scale in the transitional regime.
