论文标题
Langevin动力学的定量流体动力学限制梯度界面模型
Quantitative hydrodynamic limits of the Langevin dynamics for gradient interface models
论文作者
论文摘要
我们研究了对应于具有均匀凸相互潜力的$ \ nabla ϕ $（或Ginzburg-landau）界面模型的Langevin动力学。我们将这些Langevin动力学解释为白噪声强迫强迫的非线性抛物线方程，这将问题变成了非线性均质化问题。使用定量均质化方法，我们证明了定量的流体动力学极限，获得表面张力的$ C^2 $，证明对动态轨迹进行了大规模的Lipschitz-type估计，并表明可以将波动 - 隔离关系视为均质化和局限化的通勤性。最后，我们解释了为什么我们认为我们的技术可以适应变性（不均匀）凸相互潜力的设置。
We study the Langevin dynamics corresponding to the $\nablaϕ$ (or Ginzburg-Landau) interface model with a uniformly convex interaction potential. We interpret these Langevin dynamics as a nonlinear parabolic equation forced by white noise, which turns the problem into a nonlinear homogenization problem. Using quantitative homogenization methods, we prove a quantitative hydrodynamic limit, obtain the $C^2$ regularity of the surface tension, prove a large-scale Lipschitz-type estimate for the trajectories of the dynamics, and show that the fluctuation-dissipation relation can be seen as a commutativity of homogenization and linearization. Finally, we explain why we believe our techniques can be adapted to the setting of degenerate (non-uniformly) convex interaction potentials.
