论文标题
迈向平面上有源布朗粒子的全短时统计
Toward the full short-time statistics of an active Brownian particle on the plane
论文作者
论文摘要
我们研究平面上单个活性布朗粒子（ABP）的位置分布。我们证明该分布具有紧凑的支持，其边界是一个扩展的圆圈。我们专注于短期制度，并采用最佳波动方法（OFM）来研究粒子位置的巨大偏差，坐标$ x $和$ y $。我们确定ABP的最佳路径，以达到$ x $和$ y $的指定值以及边际分布的$ x $和$ y $的大偏差功能。这些边际分布与$ x $和$ y $ $ $ $ $ $ $的典型波动的“接近尾巴”不断匹配。我们还计算了一个特殊的“零噪声”点附近的关节$ x $和$ y $ y $ $ p分布$ p（x，y，t）$的较大偏差功能，并表明$ \ ln p（x，x，y，t）$具有非平凡的自相似结构，作为$ x $，$ y $和$ y $ $ y $ $ y $和$ t $的函数。关节分布在扩展的圆圈中非常快地消失，在那里表现出必不可少的奇异性。这种奇异性是由边际$ x $和$ y $ distributions继承的。我们认为，短期动态的这种指纹一直存在。
We study the position distribution of a single active Brownian particle (ABP) on the plane. We show that this distribution has a compact support, the boundary of which is an expanding circle. We focus on a short-time regime and employ the optimal fluctuation method (OFM) to study large deviations of the particle position coordinates $x$ and $y$. We determine the optimal paths of the ABP, conditioned on reaching specified values of $x$ and $y$, and the large deviation functions of the marginal distributions of $x$, and of $y$. These marginal distributions match continuously with "near tails" of the $x$ and $y$ distributions of typical fluctuations, studied earlier. We also calculate the large deviation function of the joint $x$ and $y$ distribution $P(x,y,t)$ in a vicinity of a special "zero-noise" point, and show that $\ln P(x,y,t)$ has a nontrivial self-similar structure as a function of $x$, $y$ and $t$. The joint distribution vanishes extremely fast at the expanding circle, exhibiting an essential singularity there. This singularity is inherited by the marginal $x$- and $y$-distributions. We argue that this fingerprint of the short-time dynamics remains there at all times.
