论文标题
在谐波井中活跃的布朗粒子的分析溶液
Analytic Solution of an Active Brownian Particle in a Harmonic Well
论文作者
论文摘要
我们为时间依赖性的fokker-planck方程提供了一个分析解决方案，用于将二维活性布朗粒子捕获在各向同性谐波电位中。使用被动的布朗粒子作为基础，我们表明fokker-Planck操作员变成较低的对角线，这意味着特征值不受活动的影响。然后将繁殖物表示为平衡本征的组合与重量遵守精确迭代关系的权重。我们表明，对于低阶相关函数，例如位置自相关函数，递归以有限顺序在péclet数中终止，从而使我们能够生成精确的紧凑表达式并得出速度自相关函数以及时间相关的扩散系数。后者量的非单调行为是非平衡动力学的指纹。
We provide an analytical solution for the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle trapped in an isotropic harmonic potential. Using the passive Brownian particle as basis states we show that the Fokker-Planck operator becomes lower diagonal, implying that the eigenvalues are unaffected by the activity. The propagator is then expressed as a combination of the equilibrium eigenstates with weights obeying exact iterative relations. We show that for the low-order correlation functions, such as the positional autocorrelation function, the recursion terminates at finite order in the Péclet number allowing us to generate exact compact expressions and derive the velocity autocorrelation function and the time-dependent diffusion coefficient. The nonmonotonic behavior of latter quantities serves as a fingerprint of the non-equilibrium dynamics.
