Multidimensional stationary probability distribution for interacting active particles

• Published in: Scientific reports Vol. 5; no. 1; p. 10742
• Main Authors: Maggi, Claudio, Marconi, Umberto Marini Bettolo, Gnan, Nicoletta, Di Leonardo, Roberto
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 29.05.2015; Nature Publishing Group
• Subjects: 639/766/530; 639/766/747; Humanities and Social Sciences; multidisciplinary; Noise; Probability distribution; Scaling; Science
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/srep10742

We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a multidimensional version of the Unified Colored Noise Approximation. By comparing theory with numerical simulations we demonstrate that the theoretical probability density quantitatively describes the accumulation of active particles around repulsive obstacles. In particular, for two particles with repulsive interactions, the probability of close contact decreases when one of the two particle is pinned. Moreover, in the case of isotropic confining potentials, the radial density profile shows a non trivial scaling with radius. Finally we show that the theory well approximates the “pressure” generated by the active particles allowing to derive an equation of state for a system of non-interacting colored noise-driven particles.