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We analyzed particle displacements in granular systems, revealing ergodicity breaking due to particle size and mass variations. Our findings align with simulations, offering insights into complex granular dynamics.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Granular Materials

Background:

  • Granular systems exhibit complex behaviors distinct from simple fluids.
  • Understanding particle dynamics is crucial for predicting material properties.
  • Ergodicity breaking is a key phenomenon in non-equilibrium systems.

Purpose of the Study:

  • To investigate ensemble and time-averaged mean-squared displacements in polydisperse granular systems.
  • To derive analytical expressions for particle displacements across different time scales.
  • To identify and explain ergodicity breaking in these systems.

Main Methods:

  • Derivation of rigorous analytical expressions for mean-squared displacements.
  • Analysis of homogeneous cooling states in polydisperse granular systems.
  • Comparison with Monte Carlo simulations using a low-rank algorithm.

Main Results:

  • Analytical expressions for ensemble and time-averaged mean-squared displacements were derived.
  • Discrepancies between ensemble and time-averaged displacements confirm ergodicity breaking.
  • The study considered granular systems with an arbitrary number of species, sizes, and masses.

Conclusions:

  • Ergodicity breaking is a characteristic feature of polydisperse granular systems.
  • The derived analytical expressions accurately describe particle dynamics.
  • The findings are validated by strong agreement with Monte Carlo simulations.