单文件系统中的广义密度分布
Generalised density profiles in single-file systems
摘要：
单列扩散是指粒子在狭窄通道中的运动，这些粒子不能绕过彼此。粒子之间的这些强相关性导致示踪剂亚扩散，这已经在多孔介质、沸石或受限胶体悬浮液中的运输等不同的背景下观察到，并且在许多作品中进行了理论研究。对这个著名的多体问题的大多数方法仅限于示踪剂的描述，示踪剂的基本性质，如大偏差函数或两次关联函数，直到最近才被确定。在这里，我们超越了这个标准的描述，通过引入和确定分析广义密度分布（GDP）的框架中的示踪剂。除了控制示踪剂的统计特性之外，这些量还充分地证实了示踪剂位置与熔池颗粒密度之间的相关性。考虑到问题的流体动力学限制，我们揭示了普遍的缩放性质的GDP与空间和时间，和非单调的依赖性与距离的示踪剂，尽管没有任何不对称。我们的分析方法提供了精确的结果的GDPs的范式模型的单列扩散，如布朗粒子与硬核排斥，对称排斥过程和随机平均过程。我们的方法的适用范围进一步说明考虑扩展到一般粒子之间的相互作用和平衡的情况。
英文摘要：
Single-file diffusion refers to the motion in narrow channels of particles which cannot bypass each other. These strong correlations between particles lead to tracer subdiffusion, which has been observed in contexts as varied as transport in porous media, zeolites or confined colloidal suspensions, and theoretically studied in numerous works. Most approaches to this celebrated many-body problem were restricted to the description of the tracer only, whose essential properties, such as large deviation functions or two-time correlation functions, were determined only recently. Here, we go beyond this standard description by introducing and determining analytically generalised density profiles (GDPs) in the frame of the tracer. In addition to controlling the statistical properties of the tracer, these quantities fully characterise the correlations between the tracer position and the bath particles density. Considering the hydrodynamic limit of the problem, we unveil universal scaling properties of the GDPs with space and time, and a non-monotonic dependence with the distance to the tracer despite the absence of any asymmetry. Our analytical approach provides exact results for the GDPs of 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 extensions to general interactions between particles and out-of-equilibrium situations.
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