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Fluctuations of one-dimensional Ginzburg-Landau models in nonequilibrium. (English) Zbl 0754.76006

Summary: We study the fluctuation of one-dimensional Ginzburg-Landau models in nonequilibrium along the hydrodynamic (diffusion) limit. The hydrodynamic limit has been proved to be a nonlinear diffusion equation by J. Fritz [Probab. Theory Relat. Fields 81, No. 2, 291-318 (1989; Zbl 0665.60108)], M. Z. Guo, G. C. Papanicolaou and S. R. S. Varadhan [Commun. Math. Phys. 118, No. 1, 31-59 (1988; Zbl 0652.60107)], etc. We proved that if the potential is uniformly convex then the fluctuation process is governed by an Ornstein-Uhlenbeck process whose drift term is obtained by formally linearizing the hydrodynamic equation.

MSC:

76A05 Non-Newtonian fluids
35Q55 NLS equations (nonlinear Schrödinger equations)
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
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