Hydrodynamic restrict for the Ginzburg-Landau ∇φ interface mannequin with non-convex potential
Authors: Jean-Dominique Deuschel, Takao Nishikawa, Yvon Vignaud
Summary: Hydrodynamic restrict for the Ginzburg-Landau ∇φ interface mannequin was established in [Nishikawa, 2003] below the Dirichlet boundary situations. This paper research the same drawback, however with non-convex potentials. Due to the dearth of strict convexity, loads of difficulties come up, particularly, on the identification of equilibrium states. We give a proof of the equivalence between the stationarity and the Gibbs property below fairly common settings, and as its conclusion, we full the identification of equilibrium states below the excessive temparature regime in [Deuschel and Cotar, 2008]. We additionally set up some uniform estimates for variances of extremal Gibbs measures below fairly common settings. △
