论文标题
谐波陷阱中的活性布朗粒子：矩的精确计算和重点过渡
Active Brownian particle in harmonic trap: exact computation of moments, and re-entrant transition
论文作者
论文摘要
在存在翻译扩散的情况下，我们考虑了$ d $维的谐波陷阱中的一个活跃的布朗粒子。虽然通常无法求解Fokker-Planck方程来获得位置和方向的联合分布的封闭形式解决方案，但我们可以使用Laplace Transform使用一种方法来评估所有矩的确切时间依赖性。我们在任意时间介绍了几个这样的时刻的明确计算，并将其演变成稳态。特别是我们计算了位移的峰度，该数量清楚地显示了与高斯均衡形式相比的差异。我们发现它随着渐近饱和度而增加，但随着陷阱 - 敏捷性而非单调的变化，从而捕获了最近观察到的活跃的被动重点行为。
We consider an active Brownian particle in a $d$-dimensional harmonic trap, in the presence of translational diffusion. While the Fokker-Planck equation can not in general be solved to obtain a closed form solution of the joint distribution of positions and orientations, as we show, it can be utilized to evaluate the exact time dependence of all moments, using a Laplace transform approach. We present explicit calculation of several such moments at arbitrary times and their evolution to the steady state. In particular we compute the kurtosis of the displacement, a quantity which clearly shows the difference of the active steady state properties from the equilibrium Gaussian form. We find that it increases with activity to asymptotic saturation, but varies non-monotonically with the trap-stiffness, thereby capturing a recently observed active- to- passive re-entrant behavior.
