论文标题
在二维中的谐和跑步粒子的确切位置分布
Exact position distribution of a harmonically-confined run-and-tumble particle in two dimensions
论文作者
论文摘要
我们考虑一个在二维中的过度抑制式跑步粒子，其自我推进在随机方向上以恒定的速率，顺时针或逆时针旋转90度，并以同样的概率旋转。另外，粒子被刚度$μ$的外部谐波电位限制，并且可能是扩散的。我们找到了粒子位置的确切时间依赖性分布$ p \ left（x，y，t \右）$，尤其是稳态分布$ p _ {\ text {st}} \ left（x，y \ right）$长期限制。我们还找到了“免费”粒子的$ p \ left（x，y，t \ right）$，$μ= 0 $。我们通过表明，在适当的坐标变化下，该问题分解为两个统计独立的一维问题，最近获得了确切的解决方案。然后，我们将这些结果朝多个方向扩展到两个具有谐波相互作用的运行式颗粒，并通过三个或更高的尺寸系统，并允许随机重置。
We consider an overdamped run-and-tumble particle in two dimensions, with self propulsion in an orientation that stochastically rotates by 90 degrees at a constant rate, clockwise or counter-clockwise with equal probabilities. In addition, the particle is confined by an external harmonic potential of stiffness $μ$, and possibly diffuses. We find the exact time-dependent distribution $P\left(x,y,t\right)$ of the particle's position, and in particular, the steady-state distribution $P_{\text{st}}\left(x,y\right)$ that is reached in the long-time limit. We also find $P\left(x,y,t\right)$ for a "free" particle, $μ=0$. We achieve this by showing that, under a proper change of coordinates, the problem decomposes into two statistically-independent one-dimensional problems, whose exact solution has recently been obtained. We then extend these results in several directions, to two such run-and-tumble particles with a harmonic interaction, to analogous systems of dimension three or higher, and by allowing stochastic resetting.
