发表机构
Tata Institute of Fundamental Research; International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究所; 塔塔基础研究所理论科学国际中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究对称排斥过程中渗流簇上等待时间分布，发现高密度下指数随密度连续变化，并探讨了连续等待时间的相关性。
AI 中文摘要
我们研究了在稳态下，一维和二维格点上每个格点附有侧支的对称排斥过程中硬核相互作用粒子的等待时间分布。我们使用数值模拟以及对稳态下被困在侧支中的粒子的近似解析处理。这种二维地毯作为超临界渗流簇捕获的简化模型。在高粒子密度下，系统表现出强烈的动力学异质性，等待时间对数的分布形成分离良好的峰，对应于从主干不同深度捕获的粒子。我们证明了标记粒子在时间$t_0+t$与时间$t_0$占据相同位置的概率以$t^{-\omega}$的代数方式衰减，其中指数$\omega$在密度高于阈值$\rho^*<1$时随粒子密度连续变化。我们还研究了标记粒子轨迹上连续等待时间之间的相关性。
英文摘要
We study the waiting-time distribution of hard-core interacting particles in the symmetric exclusion process on one- and two-dimensional lattices with side branches attached to each lattice site in the steady state. We use numerical simulations together with an approximate analytical treatment of particles trapped in side branches in the steady state. Such a two-dimensional carpet serves as a simplified model for trapping of a supercritical percolation cluster. At high particle densities, the system exhibits strong dynamical heterogeneity, with the distribution of logarithms of waiting times developing well-separated peaks corresponding to particles trapped at different depths from the backbone. We show that the probability that a tagged particle occupies the same position at time $t_0+t$ as at time $t_0$ decays algebraically as $t^{-ω}$, where the exponent $ω$ varies continuously with particle density for densities above a threshold value $ρ^*<1$. We also investigate the correlations between successive waiting times along the trajectory of a tagged particle.
Comments13 pages, 14 figures
