二维各向异性KPZ方程的对数超扩散系数
Logarithmic superdiffusivity of the 2-dimensional anisotropic KPZ equation
摘要：
我们研究了二维Kardar-Parisi-Zhang方程的各向异性变体，该变体与描述邻面的生长有关，并且具有高斯、几何粗糙的定态。虽然民间传说的信念（基于单圈重整化群）是，该方程具有相同的标度行为的（线性）爱德华-威尔金森方程，我们证明，相反，非线性诱导出现的对数超扩散。这一现象与二维流体和受驱动粒子系统的超扩散率相似。
英文摘要：
We study an anisotropic variant of the two-dimensional Kardar-Parisi-Zhang equation, that is relevant to describe growth of vicinal surfaces and has Gaussian, logarithmically rough, stationary states. While the folklore belief (based on one-loop Renormalization Group) is that the equation has the same scaling behaviour as the (linear) Edwards-Wilkinson equation, we prove that, on the contrary, the non-linearity induces the emergence of a logarithmic super-diffusivity. This phenomenon is similar in flavour to the super-diffusivity for two-dimensional fluids and driven particle systems.
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