Synchronization of oscillators with long range power law interactions - Condensed Matter > Statistical Mechanics

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Abstract: We present analytical calculations and numerical simulations for thesynchronization of oscillators interacting via a long range power lawinteraction on a one dimensional lattice. We have identified the critical valueof the power law exponent $\alpha c$ across which a transition from asynchronized to an unsynchronized state takes place for a sufficiently strongbut finite coupling strength in the large system limit. We find $\alpha c=3-2$.Frequency entrainment and phase ordering are discussed as a function of $\alpha\geq 1$. The calculations are performed using an expansion about the alignedphase state spin-wave approximation and a coarse graining approach. We alsogeneralize the spin-wave results to the {\it d}-dimensional problem.

Autor: Debanjan Chowdhury, M. C. Cross

Fuente: https://arxiv.org/