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Superdiffusion, large-scale synchronization, and topological defects.

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We investigated how random walker motion affects synchronized oscillators. Superdiffusion promotes long-range order by suppressing defects, unlike normal diffusion which leads to quasi-long-range order.

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Area of Science:

  • Statistical physics
  • Complex systems
  • Nonlinear dynamics

Background:

  • Coupled oscillators exhibit emergent synchronization.
  • Random motion introduces fluctuations and nonequilibrium dynamics.
  • Understanding order emergence in mobile systems is crucial.

Purpose of the Study:

  • To analyze the impact of random walker motion on oscillator synchronization.
  • To investigate how normal diffusion and superdiffusion affect order formation.
  • To develop a theoretical framework for nonequilibrium dynamics in mobile systems.

Main Methods:

  • Developed a non-Hamiltonian field theory with multiplicative noise.
  • Analyzed dynamics for normal diffusive and superdiffusive motion.
  • Utilized particle-based simulations for validation.

Main Results:

  • Normal diffusion in 2D leads to a defect-mediated transition to quasi-long-range order.
  • Superdiffusion in 2D suppresses topological defects, enabling continuous transition to long-range order.
  • Synchronization properties show power-law dependence on system size for normal diffusion.

Conclusions:

  • Random walker mobility significantly influences the type and range of emergent order.
  • Superdiffusion offers a pathway to robust long-range synchronization in 2D systems.
  • The derived field theory accurately describes the macroscale nonequilibrium dynamics.