Superdiffusive trajectories in Brownian motion

Duplat, Jerome
Kheifets, Simon
Li, Tongcang
Raizen, Mark G.
Villermaux, Emmanuel
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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

Duplat, Jérôme, Simon Kheifets, Tongcang Li, Mark G. Raizen, and Emmanuel Villermaux. "Superdiffusive trajectories in Brownian motion." Physical Review E 87, no. 2 (2013): 020105.