Brownian Motion with Active Fluctuations

Pawel Romanczuk and Lutz Schimansky-Geier
Phys. Rev. Lett. 106, 230601 – Published 8 June 2011


We study the effect of different types of fluctuation on the motion of self-propelled particles in two spatial dimensions. We distinguish between passive and active fluctuations. Passive fluctuations (e.g., thermal fluctuations) are independent of the orientation of the particle. In contrast, active ones point parallel or perpendicular to the time dependent orientation of the particle. We derive analytical expressions for the speed and velocity probability density for a generic model of active Brownian particles, which yields an increased probability of low speeds in the presence of active fluctuations in comparison to the case of purely passive fluctuations. As a consequence, we predict sharply peaked Cartesian velocity probability densities at the origin. Finally, we show that such a behavior may also occur in non-Gaussian active fluctuations and discuss briefly correlations of the fluctuating stochastic forces.

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  • Received 9 November 2010


© 2011 American Physical Society

Authors & Affiliations

Pawel Romanczuk* and Lutz Schimansky-Geier

  • Institute of Physics, Humboldt University at Berlin, Newtonstraße 15, 12489 Berlin, Germany

  • *Present address: Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany.

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Vol. 106, Iss. 23 — 10 June 2011

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