Superdiffusive trajectories in Brownian motion

被引:22
|
作者
Duplat, Jerome [1 ]
Kheifets, Simon [2 ,3 ]
Li, Tongcang [2 ,3 ]
Raizen, Mark G. [2 ,3 ]
Villermaux, Emmanuel [4 ]
机构
[1] INAC, CEA UJF Grenoble 1, UMR E 9004, Serv Basses Temp, F-38054 Grenoble, France
[2] Univ Texas Austin, Ctr Nonlinear Dynam, Austin, TX 78712 USA
[3] Univ Texas Austin, Dept Phys, Austin, TX 78712 USA
[4] Aix Marseille Univ, Inst Rech Phenomenes Hors Equilibre, F-13384 Marseille 13, France
来源
PHYSICAL REVIEW E | 2013年 / 87卷 / 02期
关键词
PAIR DISPERSION;
D O I
10.1103/PhysRevE.87.020105
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
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, < x(2)> similar to t(2) at short-time scales, and diffusive motion < x(2)> similar to 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 < x(2)> similar to 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. DOI: 10.1103/PhysRevE.87.020105
引用
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页数:4
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