Generalized Correlation Profiles in Single-File Systems,Physical Review Letters

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Generalized Correlation Profiles in Single-File Systems
Physical Review Letters ( IF 8.1 ) Pub Date : 2021-11-24 , DOI: 10.1103/physrevlett.127.220601
Alexis Poncet _{1,

2} , Aurélien Grabsch ₁ , Pierre Illien ₃ , Olivier Bénichou ₁

Affiliation

Single-file diffusion refers to the motion in narrow channels of particles which cannot bypass each other, and leads to tracer subdiffusion. Most approaches to this celebrated many-body problem were restricted to the description of the tracer only. Here, we go beyond this standard description by introducing and providing analytical results for generalized correlation profiles (GCPs) in the frame of the tracer. In addition to controlling the statistical properties of the tracer, these quantities fully characterize the correlations between the tracer position and the bath particles density. Considering the hydrodynamic limit of the problem, we determine the scaling form of the GCPs with space and time, and unveil a nonmonotonic dependence with the distance to the tracer despite the absence of any asymmetry. Our analytical approach provides several exact results for the GCPs for paradigmatic models of single-file diffusion, such as Brownian particles with hardcore repulsion, the symmetric exclusion process and the random average process. The range of applicability of our approach is further illustrated by considering (i) extensions to general interactions between particles, (ii) the out-of-equilibrium situation of an initial step of density, and (iii) beyond the hydrodynamic limit, the GCPs at arbitrary time in the dense limit.

中文翻译：

单文件系统中的广义相关配置文件

单列扩散是指粒子在狭窄通道中不能相互绕过的运动，并导致示踪剂亚扩散。大多数解决这个著名的多体问题的方法仅限于对示踪剂的描述。在这里，我们通过在跟踪器的框架中引入和提供广义相关性配置文件 (GCP) 的分析结果来超越此标准描述。除了控制示踪剂的统计特性外，这些量还充分表征了示踪剂位置与熔池颗粒密度之间的相关性。考虑到问题的流体力学限制，我们确定了 GCP 随空间和时间的缩放形式，并揭示了与示踪剂距离的非单调依赖性，尽管不存在任何不对称性。我们的分析方法为单文件扩散的范式模型的 GCP 提供了几个精确的结果，例如具有硬核排斥的布朗粒子、对称排除过程和随机平均过程。我们的方法的适用范围通过考虑 (i) 粒子之间一般相互作用的扩展，(ii) 初始密度步长的不平衡情况，以及 (iii) 超出流体动力学极限，GCP 得到进一步说明在密集极限中的任意时间。

更新日期：2021-11-24

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