Many-body theory of synchronization by long-range interactions

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Synchronization of coupled oscillators on a d-dimensional lattice with the power-law coupling G(r)=g0/rα and randomly distributed intrinsic frequency is analyzed. A systematic perturbation theory is developed to calculate the order parameter profile and correlation functions in powers of ε=α/d-1. For α≤d, the system exhibits a sharp synchronization transition as described by the conventional mean-field theory. For α>d, the transition is smeared by the quenched disorder, and the macroscopic order parameter ψ̄ decays slowly with g0 as |ψ̄| g02.

Original languageEnglish
Article number064101
JournalPhysical Review Letters
Issue number6
Publication statusPublished - 2011 Feb 8


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