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Universal Critical Behavior of Noisy Coupled Oscillators

Thomas Risler·Jacques Prost·Frank Julicher
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Abstract

We study the universal thermodynamic properties of systems consisting of many coupled oscillators operating in the vicinity of a homogeneous oscillating instability. In the thermodynamic limit, the Hopf bifurcation is a dynamic critical point far from equilibrium described by a statistical field theory. We perform a perturbative renormalization group study, and show that at the critical point a generic relation between correlation and response functions appears. At the same time the fluctuation-dissipation relation is strongly violated.

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Thomas Risler, Jacques Prost, Frank Julicher. 2004-09-17. Universal Critical Behavior of Noisy Coupled Oscillators. https://doi.org/10.1103/physrevlett.93.175702

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