Non-Gaussian behaviour of a self-propelled particle on a substrate

Details Non-Gaussian behaviour of a self-propelled particle on a substrate Non-Gaussian behaviour of a self-propelled particle on a substrate

2009-06-18

arxiv.org/abs/0906.3418v1

Condensed Matter Physics, 12, 725 (2009)

Physics

Condensed Matter

Soft Condensed Matter

20 pages, 10 figures

Scientific paper

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 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.

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