Condensed Matter Physics, 2009, vol. 12, No. 4, pp. 725-738
DOI:10.5488/CMP.12.4.725
Title:
Non-Gaussian behaviour of a self-propelled particle on a substrate
Author(s):
 
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B. ten Hagen
(Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany)
,
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S. van Teeffelen
(Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany)
,
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H. Löwen
(Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany)
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The overdamped Brownian motion of a self-propelled particle which is driven by a projected internal force is studied by solving the Langevin equation analytically. The "active" particle under study is restricted to move along a linear channel. The direction of its internal force is orientationally diffusing on a unit circle in a plane perpendicular to the substrate. An additional time-dependent torque is acting on the internal force orientation. The model is relevant for active particles like catalytically driven Janus particles and bacteria moving on a substrate. Analytical results for the first four time-dependent displacement moments are presented and analysed for several special situations. For a vanishing torque, there is a significant dynamical non-Gaussian behaviour at finite times t as signalled by a non-vanishing normalized kurtosis in the particle displacement which approaches zero for long time with a 1/t long-time tail.
Key words:
Brownian dynamics, self-propelled particle, substrate, swimmer, active particles, diffusion
PACS:
82.70.Dd, 05.40.Jc
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