title: Synchronization of oscillators with long-range power law interactions.
abstract: We present analytical calculations and numerical simulations for the synchronization of oscillators interacting via a long-range power law interaction on a one-dimensional lattice. We have identified the critical value of the power law exponent α(c) across which a transition from a synchronized to an unsynchronized state takes place for a sufficiently strong but finite coupling strength in the large system limit. We find α(c)=3/2. Frequency entrainment and phase ordering are discussed as a function of α≥1 . The calculations are performed using an expansion about the aligned phase state (spin-wave approximation) and a coarse graining approach. We also generalize the spin-wave results to the d -dimensional problem.
authors.affiliation: Department of Physics, California Institute of Technology, Pasadena, California 91125, USA. debanjanchowdhury@gmail.com
authors.forename: Debanjan
authors.initials: D
authors.lastname: Chowdhury
authors.forename: M C
authors.initials: MC
authors.lastname: Cross