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Effective ergodicity breaking phase transition in a driven-dissipative system.

Sakib Matin1, Chon-Kit Pun1, Harvey Gould1,2

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This summary is machine-generated.

The Olami-Feder-Christensen model shows a transition from ergodic to non-ergodic behavior as noise changes. This ergodicity breaking transition is characterized by changes in site stress and recurrence rates.

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Area of Science:

  • Complex systems
  • Statistical physics
  • Dynamical systems

Background:

  • The Olami-Feder-Christensen (OFC) model is a sandpile model known for exhibiting self-organized criticality.
  • Understanding the conditions under which such models transition between different dynamical regimes is crucial for complex systems research.

Purpose of the Study:

  • To investigate the phenomenon of ergodicity breaking in the OFC model.
  • To characterize the transition using concepts from dynamical systems and percolation theory.

Main Methods:

  • Numerical simulations of the OFC model.
  • Analysis of time-averaged stress on individual sites.
  • Computation of recurrence plots and recurrence rates from dynamical system theory.
  • Examination of clusters of failed sites using percolation theory.

Main Results:

  • A clear transition to effective ergodicity breaking was observed as noise intensity was varied.
  • Below a critical noise level, individual site stresses were trapped in limit cycles, indicating non-ergodicity.
  • The average recurrence rate across all sites was identified as an order parameter, showing a distinct jump at the critical noise.
  • Exponents characterizing the transition from above were found to be consistent with hyperscaling relations.

Conclusions:

  • The OFC model exhibits an effective ergodicity breaking transition driven by noise intensity.
  • Dynamical system measures like recurrence plots effectively characterize this transition.
  • The transition shares characteristics with universality classes found in percolation theory.