Critical phenomena far from equilibrium

Abstract

Stationary regimes of active systems—those in which dissipation is compensated by pumping—are considered. Approaching the bifurcation point of such a regime leads to an increase in susceptibility, with soft modes making the dominant contribution. Weak noise, which is inherent to any real system, increases. Sufficiently close to bifurcation, the amplitude of random pulsations is comparable to the average value of the fluctuating quantity, as in the case of developed turbulence. The spectrum of critical pulsations is independent of the original noise. Numerical simulation of the neighborhood of a bifurcation point is considered unreliable because of the poor reproducibility of results. Due to the high susceptibility, calculation roundings result in ‘chaotic’ jumps of the solution in response to a smooth change in the parameters. It is therefore necessary in the simulation process to introduce a small random function of time, white noise. The solutions of the Langevin equations obtained in this way should be processed statistically. Their properties (except for the intensity of pulsations) are independent of the noise induced. Examples of the statistical description of bifurcations are given.