Unfolding tagged particle histories in single-file diffusion: exact single- and two-tag local times beyond large deviation theory
Unfolding tagged particle histories in single-file diffusion: exact single- and two-tag local times beyond large deviation theory
复制标题
在单列扩散中展开标记粒子历史：超越大偏差理论的精确单标记和双标记局部时间
DOI：
10.1088/1367-2630/aaea1b
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发表时间：
2018
影响因子：
3.3
通讯作者：
A. Godec
中科院分区：
文献类型：
--
作者：
Alessio Lapolla;A. Godec
粒子之间的强位置相关性使得示踪剂粒子在单个文件中的扩散异常且非马尔可夫。虽然示踪粒子的系综平均可观量现在已经被很好地理解，但对相应泛函的统计，即时间平均可观量却知之甚少。甚至还不清楚非马尔科夫性质是如何从不同时间粒子轨迹之间的关联中出现的。在这里，我们首先给出了具有可对角化传播算子的遍历马尔可夫过程的一般有界泛函的涨落和双标记关联的严格结果。它们将任意时间尺度上泛函的统计与松弛本征谱联系起来。然后，我们研究了标记粒子的局部时间--示踪粒子在沿着单个轨迹的某个预定位置停留到时间t的时间。对于单标记和双标记的局部时间，我们得到了精确的结果，这揭示了单个粒子的历史如何在更高的密度下变得相关，因为沿轨迹的每个连续位移都需要集体重排。我们的结果揭示了轨迹水平上投影诱导记忆的复杂含义，对于总体平均可观测性是不可见的，并允许对探测标记粒子探索统计的单文件实验进行详细分析。
Strong positional correlations between particles render the diffusion of a tracer particle in a single file anomalous and non-Markovian. While ensemble average observables of tracer particles are nowadays well understood, little is known about the statistics of the corresponding functionals, i.e. the time-average observables. It even remains unclear how the non-Markovian nature emerges from correlations between particle trajectories at different times. Here, we first present rigorous results for fluctuations and two-tag correlations of general bounded functionals of ergodic Markov processes with a diagonalizable propagator. They relate the statistics of functionals on arbitrary time-scales to the relaxation eigenspectrum. Then we study tagged particle local times—the time a tracer particle spends at some predefined location along a single trajectory up to a time t. Exact results are derived for one- and two-tag local times, which reveal how the individual particles’ histories become correlated at higher densities because each consecutive displacement along a trajectory requires collective rearrangements. Our results unveil the intricate meaning of projection-induced memory on a trajectory level, invisible to ensemble-average observables, and allow for a detailed analysis of single-file experiments probing tagged particle exploration statistics.