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Density relaxation in conserved Manna sandpiles.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Condensed Matter Physics

Background:

  • The Manna sandpile model is a 1D system used to study self-organized criticality.
  • Understanding relaxation dynamics is crucial for characterizing system behavior far from and near critical points.

Purpose of the Study:

  • To analyze the relaxation of long-wavelength density perturbations in a 1D conserved Manna sandpile.
  • To investigate diffusive and anomalous transport regimes and their impact on relaxation times.
  • To determine the scaling behavior of density perturbations near criticality.

Main Methods:

  • Analytical calculations of density profile relaxation.
  • Theoretical analysis of diffusive and anomalous transport coefficients.
  • Derivation of scaling laws for perturbation width growth.

Main Results:

  • Far from criticality, relaxation is diffusive (τR∼k⁻²/D).
  • Near criticality, anomalous transport leads to τR∼k⁻ᶻ, with z<2.
  • Localized perturbations on a critical background exhibit self-similar relaxation with anomalous width growth (σ∼tω, ω>1/2).

Conclusions:

  • Theoretical predictions for relaxation dynamics and scaling behavior are in good agreement with simulations.
  • The study reveals distinct relaxation mechanisms in diffusive and anomalous transport regimes.
  • Anomalous diffusion and self-similar structures characterize sandpile dynamics near criticality.