论文标题
在任意空间维度中堵塞多个持续的随机步行者
Jamming of multiple persistent random walkers in arbitrary spatial dimension
论文作者
论文摘要
我们考虑了持续的排除过程，其中一组持续的随机步行者通过$ d $ dimensions中的高立管晶格上的硬核排除通过硬核排除进行交互。我们在弹道制度内工作，从而在重新定位之前，颗粒继续在许多晶格站点上朝着相同的方向跳跃。在两个粒子的情况下，我们找到了平均第一次通用时间到堵塞的状态，颗粒占据相邻位点并彼此面对。这是在近似值中实现的，等同于将一维系统嵌入更高的储层中。数值结果证明了这种近似值的有效性，即使对于小晶格也是如此。结果承认了一个直接的概括，以稀释包含两个以上粒子的系统。这些结果的有效性的自矛盾条件表明，与在扩散极限中发现的相比，弹性策略中的簇可能以任意低的密度形成。
We consider the persistent exclusion process in which a set of persistent random walkers interact via hard-core exclusion on a hypercubic lattice in $d$ dimensions. We work within the ballistic regime whereby particles continue to hop in the same direction over many lattice sites before reorienting. In the case of two particles, we find the mean first-passage time to a jammed state where the particles occupy adjacent sites and face each other. This is achieved within an approximation that amounts to embedding the one-dimensional system in a higher-dimensional reservoir. Numerical results demonstrate the validity of this approximation, even for small lattices. The results admit a straightforward generalisation to dilute systems comprising more than two particles. A self-consistency condition on the validity of these results suggest that clusters may form at arbitrarily low densities in the ballistic regime, in contrast to what has been found in the diffusive limit.
