Dynamical bifurcation with noise
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It was shown by A. Neishtadt that dynamical bifurcation, in which the control parameter is varied with a small but finite speed ∈, is characterized by adelay in bifurcation, here denoted λj and depending on ∈. Here we study dynamical bifurcation, in the framework and with the language of Landau theory of phase transitions, in the presence of a Gaussian noise of strength σ. By numerical experiments at fixed ∈ = ∈0, we study the dependence of λj on a for order parameters of dimension ≤3; an exact scaling relation satisfied by the equations permits us to obtain for this the behavior for general ∈. We find that in the smallnoise regime λj(σ) ≃aσ(−b), while in the strong-noise regime λj(σ) − ce(−d); we also measure the parameters in these formulas.
KeywordsPhase Transition Field Theory Elementary Particle Quantum Field Theory Numerical Experiment
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