Amplification by globally coupled arrays: Coherence and symmetry

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Abstract
We study the general problem of small-signal amplification by globally coupled oscillator arrays. The analysis is relevant, for example, to series-array Josephson-junction parametric amplifiers and to certain multimode laser systems. Maximum amplification is achieved near symmetry-preserving bifurcations; the response near symmetry-breaking bifurcations is substantially worse. In the presence of noise, we find a seemingly paradoxical phenomenon wherein individual array elements suffer large-scale random fluctuations, yet the total array response remains steady.