The symmetric exclusion process (SEP), where particles hop on a one-dimensional lattice with the restriction that there can only be one particle per site, is a paradigmatic model of interacting particle systems. Recently, it has been shown that the nature of the initial conditions—annealed or quenched—has a quantitative impact on the long-time properties of tracer diffusion. However, so far, the cumulant generating function in the quenched case was only determined in the low-density limit and for the specific case of a half-filled system. Here, we derive it in the opposite dense limit with quenched initial conditions. Importantly, our approach also allows us to consider the nonequilibrium situations of (i) a biased tracer in the SEP and (ii) a symmetric tracer in a step of density. In the former situation, we show that the initial conditions have a striking impact, and change the very dependence of the cumulants on the bias.

中文翻译：

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示踪剂在猝灭密集对称排除过程中的累积量生成功能

对称排斥过程（SEP）是粒子在一个一维晶格上跳跃并且每个站点只能有一个粒子的限制，它是相互作用的粒子系统的范式模型。最近，已经表明，退火或淬火的初始条件的性质对示踪剂扩散的长期特性具有定量影响。但是，到目前为止，在淬火情况下的累积量生成功能仅在低密度限制下确定，并且对于半填充系统的特定情况才确定。在这里，我们在淬火的初始条件下以相反的密度极限来导出它。重要的是，我们的方法还使我们能够考虑（i）SEP中有偏差的示踪剂和（ii）密度阶梯中的对称示踪剂的非平衡情况。在前一种情况下，