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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Intermittent stochastic motion, alternating between two states, is prevalent in physical and biological systems.
  • Existing theories struggle to comprehensively describe this dichotomous process.
  • A need exists for generalized models capturing diverse intermittent behaviors.

Purpose of the Study:

  • Introduce a generalized intermittent random walk model.
  • Analyze anomalous diffusion, aging, and ergodicity in intermittent processes.
  • Investigate the coexistence of ergodicity and nonergodicity.

Main Methods:

  • Developed a renewal process model alternating between Continuous Time Random Walk (CTRW) and generalized Lévy walk (gLW) states.
  • Utilized nonlinear space-time coupling inherent in gLW.
  • Derived velocity correlation function and applied scaling Green-Kubo relation.

Main Results:

  • Calculated ensemble-averaged and time-averaged mean-squared displacement (MSD).
  • Identified two diffusive terms in MSD, with diffusion characterized by the largest diffusion coefficient.
  • Demonstrated coexistence of ergodicity and nonergodicity due to intermittent characteristics.

Conclusions:

  • The generalized model encompasses various random walk models.
  • Intermittent processes exhibit unique diffusive behavior distinct from single-state processes.
  • Power-law sojourn times, nonlinear coupling, and intermittency enable coexistence of ergodicity and nonergodicity.