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Updated: Jul 30, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Dynamical fluctuations in the Riesz gas
Rahul Dandekar1, P L Krapivsky2,3, Kirone Mallick1
1Institut de Physique Théorique, CEA Paris-Saclay, F-91191 Gif-sur-Yvette Cedex, France.
Abstract:
We consider an infinite system of particles on a line performing identical Brownian motions and interacting through the |x-y|^{-s} Riesz potential, causing the overdamped motion of particles. We investigate fluctuations of the integrated current and the position of a tagged particle. We show that for 01, the interactions are effectively short-ranged, and the universal subdiffusive t^{1/4} growth emerges with only amplitude depending on the exponent s. We also show that the two-time correlations of the tagged-particle position have the same form as for fractional Brownian motion.
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