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Area of Science:

  • Statistical Mechanics
  • Mathematical Physics
  • Stochastic Processes

Background:

  • Brownian motion describes random particle movement.
  • Riesz potentials model interactions in physical systems.
  • Understanding particle system dynamics is crucial in physics.

Purpose of the Study:

  • Investigate fluctuations in integrated current and tagged particle position.
  • Analyze the impact of Riesz potential interactions on particle dynamics.
  • Determine the scaling laws for these fluctuations based on interaction exponent 's'.

Main Methods:

  • Considered an infinite system of particles on a line undergoing Brownian motion.
  • Modeled particle interactions using the |x-y|^{-s} Riesz potential.
  • Analyzed overdamped motion and derived scaling behaviors for fluctuations.

Main Results:

  • For 0
  • For s>1, a universal subdiffusive t^{1/4} growth emerges.
  • Tagged-particle position correlations match fractional Brownian motion.

Conclusions:

  • Interaction range significantly influences particle system fluctuations.
  • A transition in scaling behavior occurs at s=1.
  • The system exhibits properties analogous to fractional Brownian motion.