Semi-infinite Simple Exclusion Process: From Current Fluctuations to Target Survival,Physical Review Letters

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Semi-infinite Simple Exclusion Process: From Current Fluctuations to Target Survival
Physical Review Letters ( IF 8.1 ) Pub Date : 2024-09-10 , DOI: 10.1103/physrevlett.133.117102
Aurélien Grabsch _{1,

2} , Hiroki Moriya _{1,

2} , Kirone Mallick ₃ , Tomohiro Sasamoto ₄ , Olivier Bénichou _{1,

2}

Affiliation

The symmetric simple exclusion process (SEP), where diffusive particles cannot overtake each other, is a paradigmatic model of transport in the single-file geometry. In this model, the study of currents has attracted a lot of attention, but so far most results are restricted to two geometries: (i) a finite system between two reservoirs, which does not conserve the number of particles but reaches a nonequilibrium steady state, and (ii) an infinite system which conserves the number of particles but never reaches a steady state. Here, we obtain an expression for the full cumulant generating function of the integrated current in the important intermediate situation of a semi-infinite system connected to a reservoir, which does not conserve the number of particles and never reaches a steady state. This results from the determination of the full spatial structure of the correlations, which we infer to obey the very same closed equation recently obtained in the infinite geometry and argue to be exact. Besides their intrinsic interest, these results allow us to solve two open problems: the survival probability of a fixed target in the SEP, and the statistics of the number of particles injected by a localized source.

中文翻译：

半无限简单排除过程：从电流波动到目标生存

对称简单排除过程（SEP）是单列几何中传输的典型模型，其中扩散粒子不能相互超越。在这个模型中，对电流的研究引起了很多关注，但到目前为止，大多数结果仅限于两种几何结构：（i）两个储库之间的有限系统，该系统不守恒粒子数量，而是达到非平衡稳态，以及（ii）一个无限系统，其粒子数量守恒，但永远不会达到稳定状态。在这里，我们获得了在连接到水库的半无限系统的重要中间情况下积分电流的完整累积量生成函数的表达式，该系统不守恒粒子数并且永远不会达到稳态。这是由于确定了相关性的完整空间结构，我们推断其遵循最近在无限几何中获得的完全相同的封闭方程，并认为是精确的。除了它们的内在兴趣之外，这些结果还使我们能够解决两个悬而未决的问题：SEP 中固定目标的生存概率，以及局部源注入的粒子数量的统计。

更新日期：2024-09-11

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