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Many-body theory of synchronization by long-range interactions
1Department of Physics, Tohoku University, Sendai 980-8578, Japan.
Physical Review Letters
|March 17, 2011
Summary
This study analyzes coupled oscillators with power-law coupling and random frequencies. For strong coupling (α > d), disorder smears synchronization, causing the order parameter to decay slowly.
Area of Science:
- Complex Systems
- Statistical Physics
- Nonlinear Dynamics
Background:
- Coupled oscillators are fundamental in many physical and biological systems.
- Understanding synchronization transitions in disordered systems is crucial.
Purpose of the Study:
- To investigate synchronization phenomena in a d-dimensional lattice of coupled oscillators.
- To analyze the effects of power-law coupling and quenched disorder on synchronization transitions.
Main Methods:
- Developed a systematic perturbation theory.
- Calculated order parameter profiles and correlation functions.
- Analyzed systems with power-law coupling G(r) = g0/rα and random intrinsic frequencies.
Main Results:
- For α ≤ d, a sharp synchronization transition occurs, consistent with mean-field theory.
- For α > d, quenched disorder smears the transition.
- The macroscopic order parameter ψ decays slowly with g0 as |ψ| ∝ g(0)(2) when α > d.
Conclusions:
- The dimensionality and coupling exponent critically influence synchronization behavior.
- Quenched disorder plays a significant role in smearing synchronization transitions in coupled oscillator systems.
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