大偏差局部聚类中的长程相关性
Long-ranged correlations in large deviations of local clustering
摘要：
在扩散粒子系统中，我们研究了一个粒子周围的时间平均聚类测量的大偏差。我们专注于有偏见的合奏轨迹，实现大偏差事件。偏置作用于单个粒子，但会产生跨越整个系统的响应。我们通过宏观涨落理论的透镜来分析这种效应，重点是偏置与流体动力学模式的耦合。这解释了在1维和2维空间中，动力学自由能与系统尺寸具有非平凡的标度关系。我们表明，长距离的反应，对一个粒子的偏见也有后果时，偏置两个粒子。
英文摘要：
In systems of diffusing particles, we investigate large deviations of a time-averaged measure of clustering around one particle. We focus on biased ensembles of trajectories, which realise large-deviation events. The bias acts on a single particle, but elicits a response that spans the whole system. We analyse this effect through the lens of Macroscopic Fluctuation Theory, focussing on the coupling of the bias to hydrodynamic modes. This explains that the dynamical free energy has non-trivial scaling relationships with the system size, in 1 and 2 spatial dimensions. We show that the long-ranged response to a bias on one particle also has consequences when biasing two particles.
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