Space Periodic Stochastic System Noise Under Non-equilibrium Phase Transitions And Transport

In this paper, by a special model, we investigate the spatially periodic stochastic system with locally coupled oscillators subject to a constant force (external force) F . This system is driven by the additive and multiplicative noises (being Gaussian white). A nonequilibrium second order phase transition is found when F = Q. This phase transition is reentrant when the additive noise is weak. Accompanying with the symmetry-breaking, a bistable solution for the nonzero mean field appears. The mean field is nonzero. At the meantimes, a nonzero flux appears. The coupling of the oscillators can induce transport of particles even in the absence of the correlation of the additive and multiplicative noises, and without the multiplicative noise. With varying the constant force F, a continuous or a discontinuous transition between thestates with positive and negative mean fields (ju > 0 and ju < 0) is observed, whichis not a phase transition. The mean field or current sometimes exhibits hysteresis as a function of F . With the variation of the force F, when hysteresis of the mean field or current versus F appears, nonzero probability current with definite direction will occur at the point F = 0. The correlation between the additive and multiplicative noises has effect on the transitions and the transport.