Universal Critical Behavior of Noisy Coupled Oscillators

Thomas Risler (1, 2) , Jacques Prost (1, 3) , Frank Julicher (2)

1 PCC - Physico-Chimie-Curie
2 MPI-PKS - Max-Planck-Institut für Physik komplexer Systeme
3 ESPCI Paris - Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris

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.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Biophysique [physics.bio-ph]

Thomas Risler, Jacques Prost, Frank Julicher. Universal Critical Behavior of Noisy Coupled Oscillators. Physical Review Letters, 2004, 93 (17), pp.175702. ⟨10.1103/PhysRevLett.93.175702⟩. ⟨hal-00961031⟩