Superdiffusive trajectories in Brownian motion.
Superdiffusive trajectories in Brownian motion.
复制标题
布朗运动中的超扩散轨迹。
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
E. Villermaux
中科院分区：
文献类型：
--
作者：
J. Duplat;Simon Kheifets;Tongcang Li;M. Raizen;E. Villermaux
流体中微观粒子的布朗运动是统计物理学的基石之一，也是随机过程的范例。朗之万提供了一个最有力的量化工具，他明确地解释了短时相关的“热”力。朗之万图像预测了短时间尺度下的弹道运动~t（2）和长时间尺度下的扩散运动~t，其中x是粒子在时间t内的位移，平均值是初始条件下的热分布。朗之万方程还预测了一个超扩散区，其中~t（3），在初始速度固定而不是热分布的条件下。我们分析了空气中光学捕获粒子的运动，并确实发现了t（3）色散。这一观察结果直接证明了朗之万所想象的随机、快速变化的力的存在。
The Brownian motion of a microscopic particle in a fluid is one of the cornerstones of statistical physics and the paradigm of a random process. One of the most powerful tools to quantify it was provided by Langevin, who explicitly accounted for a short-time correlated "thermal" force. The Langevin picture predicts ballistic motion, ~t(2) at short-time scales, and diffusive motion ~t at long-time scales, where x is the displacement of the particle during time t, and the average is taken over the thermal distribution of initial conditions. The Langevin equation also predicts a superdiffusive regime, where ~t(3), under the condition that the initial velocity is fixed rather than distributed thermally. We analyze the motion of an optically trapped particle in air and indeed find t(3) dispersion. This observation is a direct proof of the existence of the random, rapidly varying force imagined by Langevin.