论文标题
在一维扩散环境中被动粒子的演变
Evolution of a passive particle in a one-dimensional diffusive environment
论文作者
论文摘要
我们研究了由一维波动电势驱动的示踪粒子的行为，最初定义为布朗运动，并根据热方程式在及时演变。我们获得了两个主要结果。首先，在短时间内，我们表明粒子的波动变为高斯且不足，并具有动态指数$ 3/4 $。其次，在长期限制的情况下，我们表明粒子被电位的局部最小值捕获，并弥散地发展，即指数$ 1/2 $。
We study the behavior of a tracer particle driven by a one-dimensional fluctuating potential, defined initially as a Brownian motion, and evolving in time according to the heat equation. We obtain two main results. First, in the short time limit, we show that the fluctuations of the particle become Gaussian and sub-diffusive, with dynamical exponent $3/4$. Second, in the long time limit, we show that the particle is trapped by the local minima of the potential and evolves diffusively i.e. with exponent $1/2$.
