论文标题
通过波动和相关性表现出的跨界行为
Crossover behaviours exhibited by fluctuations and correlations in a chain of active particles
论文作者
论文摘要
我们研究了有源粒子的谐波链中标记的颗粒的运动。我们考虑了三种主动粒子动力学模型 - 运行和滚动粒子，活跃的Ornstein -uhlenbeck粒子和活跃的Brownian粒子。我们研究了两个标记粒子的方差，自动相关性，协方差和不等时间互相关。对于所有三种型号，我们观察到，平均平方位移从超散言的$ \ sim t^μ$缩放量表中进行了$ t \ llτ_a$（$τ_a$）的缩放（$τ_a$是由于活动而产生的时间尺度），到sub-diffusive $ \ sim \ sim \ sim \ si \ sqrt { \ frac {3} {2} $ for rtp，$μ= \ frac {5} {2} $ for aoup。对于ABP的$ x $和$ y $ - 坐标，我们分别得到$μ= \ frac {7} {2} $和$μ= \ frac {5} {2} $。我们表明，在每种情况下，这些交叉行为都可以通过连接这两个缩放制度的适当交叉函数来描述。我们明确计算这些交叉功能。此外，我们还发现，在观察时间$ t $的适当范围内，相等和不平等的时间自动和跨相关性遵守有趣的缩放表格。在所有情况下，相关的缩放函数都是严格得出的。我们所有的分析结果都得到了数值模拟的良好支持。
We study motion of tagged particles in a harmonic chain of active particles. We consider three models of active particle dynamics - run and tumble particle, active Ornstein-Uhlenbeck particle and active Brownian particle. We investigate the variance, auto correlation, covariance and unequal time cross correlation of two tagged particles. For all three models, we observe that the mean squared displacement undergoes a crossover from the super-diffusive $\sim t^μ$ scaling for $t \ll τ_A$ ($τ_A$ being the time scale arising due to the activity) to the sub-diffusive $\sim \sqrt{t}$ scaling for $t \gg τ_A$, where $μ= \frac{3}{2}$ for RTP, $μ= \frac{5}{2}$ for AOUP. For the $x$ and $y$-coordinates of ABPs we get $μ=\frac{7}{2}$ and $μ=\frac{5}{2}$ respectively. We show that these crossover behaviours in each case can be described by appropriate crossover function that connects these two scaling regimes. We compute these crossover functions explicitly. In addition, we also find that the equal and unequal time auto and cross correlations obey interesting scaling forms in the appropriate limits of the observation time $t$. The associated scaling functions are rigorously derived in all cases. All our analytical results are well supported by the numerical simulations.
