In the last years, a few experiments in the fields of biological and soft matter physics in colloidal suspensions have reported normal diffusion with a Laplacian probability distribution in the particles displacements (i.e., Brownian yet non Gaussian diffusion). To model this behavior different stochastic models had been proposed, with all of them introducing new random elements that incorporate our lack of information about the media. Although these models work in practice, due to their own nature a thorough understanding of how the media interacts with itself and with the Brownian particle in Brownian yet non Gaussian diffusion is outside of their aim and scope. For this reason, a comprehensive mathematical model to explain Brownian yet non Gaussian diffusion that includes molecular interactions is proposed in this paper. Based on the theory of interfaces by Gennes and Langevin dynamics, it is shown that long-range interactions in a weakly interacting fluid and in a microscopic regime of zero viscosity leads to a Laplacian probability distribution in the particles displacements. Further, it is shown that a phase transition can explain a high diffusivity and causes this Laplacian distribution to evolve towards a Gaussian via a transition probability in the interval of time as it was observed in experiments. To validate these model predictions, the experimental data of the Brownian motion of colloidal beads on phospholipid bilayer by Wang et al. is used and compared with the results of the theory. This comparison suggests that the proposed model not only is able to explain qualitatively the Brownian yet non-Gaussian diffusion, but also quantitatively.
Colossal Brownian yet non-Gaussian diffusion in a periodic potential: impact of nonequilibrium noise amplitude statistics
去年在[Phys. Rev. E 102，042121（2020）]中，作者研究了非平衡噪声驱动的布朗粒子在空间周期势中的过阻尼动力学，并发现了一类新的布朗扩散，但非高斯扩散。粒子的均方位移随时间线性增长，粒子位置的概率密度为高斯分布，然而，对应的增量分布为非高斯分布。后一种性质导致扩散的巨大增强，显著超过了众所周知的巨扩散效应。在这里，我们大大扩展了上述预测，通过调查的影响，非平衡噪声振幅统计的巨大布朗，但非高斯扩散。振幅分布的尾部对扩散放大的幅度以及位置和增量统计的高斯性都有重要影响。我们的研究结果进行了深刻的后果扩散行为在非平衡设置，如活细胞中的扩散是一个中央运输机制。
Three-dimensional Brownian diffusion of rod-like macromolecules in the presence of randomly distributed spherical obstacles: Molecular dynamics simulation
Broadband molecular dynamics simulation of confined Brownian motion
Université de Mons（蒙斯大学）；Univ. Bordeaux, CNRS, LOMA, UMR 5798（波尔多大学，法国国家科学研究中心，LOMA联合实验室）；University of Vienna（维也纳大学）；Ecole Polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院，巴黎理工学院）
Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking
Tokyo University of Science（东京科学大学）；Pohang University of Science and Technology（浦项科技大学）；Asia Pacific Centre for Theoretical Physics（亚太理论物理中心）；University of Potsdam（波茨坦大学）；Wakayama University（和歌山大学）；Nagoya University（名古屋大学）；Keio University（庆应义塾大学）
