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Over the past few years the displacement statistics of self-propelledparticles has been intensely studied, revealing their long-time diffusivebehavior. Here, we demonstrate that a concerted combination of boundaryconditions and switching on and off the self-propelling drive can generate andafterwards arbitrarily often restore a non-stationary centered peak in theirspatial distribution. This corresponds to a partial reversibility of theirstatistical behavior, in opposition to the above-mentioned long-time diffusivenature. Interestingly, it is a diffusive process that mediates and makespossible this procedure. It should be straightforward to verify our predictionsin a real experimental system.

Focusing by blocking: repeatedly generating central density peaks in self-propelled particle systems by exploiting diffusive processes