AI 中文总结
以一维无限有源奥恩斯坦-乌伦贝克粒子气体为模型，研究其电流涨落的大偏差统计，发现存在三种标度 regime 及初始条件的持久记忆，通过稀有事件重要性抽样验证了分析预测。
AI 中文摘要
我们研究了一维无限独立有源奥恩斯坦-乌伦贝克粒子气体中时间积分电流的统计特性，将其作为研究对应无源（扩散）现象学有源推广的模型系统。与电流涨落呈现普适亚扩散标度的无源系统不同，有源系统在不同时间尺度上表现出扩散、超扩散和亚扩散三种 regime。我们通过大偏差渐近完全表征了电流的分布，表明所有这些标度 regime 均由单一标度累积量生成函数描述。此外，该统计特性即使在长时间后仍保留对初始条件的依赖，揭示了初始状态的持续记忆。我们进一步获得了两个不同时间测得电流的联合大偏差统计特性，表征了时间相关性。我们的分析预测通过稀有事件重要性抽样得到验证，该方法可解析低至$10^{-1000}$的概率。
英文摘要
We investigate the statistics of the time-integrated current in an infinite one-dimensional gas of independent active Ornstein--Uhlenbeck particles, as a model system for studying an active generalisation of the corresponding passive (diffusive) phenomenology. Unlike the latter, where current fluctuations exhibit universal sub-diffusive scaling, active systems display diffusive, super-diffusive, and sub-diffusive regimes over different time scales. We fully characterise the distribution of current in terms of large-deviation asymptotics, showing that all of these scaling regimes are described by a single scaled cumulant generating function. Moreover, the statistics retain a dependence on the initial condition even at large times, revealing a persistent memory of the initial state. We further obtain the joint large-deviation statistics of currents measured at two distinct times, characterising temporal correlations. Our analytical predictions are verified using rare-event importance sampling, which resolves probabilities as small as $10^{-1000}$.
Comments7 Pages, 3 figures, additional 7 pages of supplementary materials
