Dandekar R, Krapivsky PL, Mallick K. Dynamical fluctuations in the Riesz gas.
Phys Rev E 2023;
107:044129. [PMID:
37198790 DOI:
10.1103/physreve.107.044129]
[Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Accepted: 02/10/2023] [Indexed: 05/19/2023]
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 0<s<1, the standard deviations of both quantities grow as t^{s/2(1+s)}. When s>1, 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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