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arXiv · 2608.27572

Scale-free correlations in extremely persistent active matter

Grzegorz Szamel
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Abstract

Scale-free correlations are believed to be generic in out of equilibrium systems but their explicit derivations are rare and often involve approximations. Here we analyze a system of infinitely persistent active Brownian particles in the low density and small-swim-velocity limit. We show that both the density and swim velocity correlations decay algebraically as r^{-(d+1)} (with logarithmic corrections in d=2). In reciprocal space these correlations manifest themselves as cusps at k=0. The analytical predictions are confirmed by numerical simulations. The results were obtained through interaction with Claude (Opus 4.8 and 5, and Fable 5) and verified by the author.

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Grzegorz Szamel. 2026-08-27. Scale-free correlations in extremely persistent active matter. https://arxiv.org/abs/2608.27572

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