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Dynamic correlations in the conserved Manna sandpile.

Anirban Mukherjee1, Punyabrata Pradhan1

  • 1Department of Physics of Complex Systems, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India.

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We investigated dynamic correlations in the Manna sandpile model, revealing subdiffusive current growth and power-law frequency dependencies for current and mass. Near criticality, this indicates dynamic hyperuniformity.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Condensed Matter Physics

Background:

  • The Manna sandpile model is a classic example of self-organized criticality.
  • Understanding dynamic correlations and fluctuations is crucial for characterizing complex systems.

Purpose of the Study:

  • To analyze dynamic correlations of current and mass in a 1D conserved Manna sandpile.
  • To investigate the power spectra of current and mass fluctuations.
  • To explore the phenomenon of dynamic hyperuniformity near criticality.

Main Methods:

  • Theoretical analysis of dynamic correlations.
  • Calculation of power spectra for current and mass.
  • Derivation of fluctuation relations.

Main Results:

  • Variance of cumulative bond current grows subdiffusively as T^{1/2-μ}.
  • Power spectra of current and mass vary as f^{1/2+μ} and f^{-3/2+μ} at low frequencies.
  • Demonstrated a quantitative relationship between fluctuations and density-dependent activity, signifying dynamic hyperuniformity near criticality.

Conclusions:

  • The study provides a theoretical framework for understanding dynamic correlations in the Manna sandpile.
  • The findings reveal a transition from normal to hyperuniform dynamics near criticality.
  • A key relation explains the scaling behavior of the self-diffusion coefficient with activity observed in simulations.