具有一般尺度不变性的二维表面中的强各向异性：非线性效应
Strong anisotropy in two-dimensional surfaces with generic scale invariance: Non-linear effects
摘要：
我们扩展了先前的研究[Phys. Rev. E 86，051611（2012）]，研究了在显示通用尺度不变性的二维表面的标度特性中发生强各向异性（SA）的条件。在那里，为SA提出了一种自然的Ancestion，它在分析来自例如薄膜生产实验的数据时自然出现。在表面动力学的高斯（线性）模型和非线性模型（如Hwa-Kardar（HK）方程[Phys. Rev. Lett. 62，1813（1989）]，这是容易通过前者的准确近似。相反，在这里，我们分析非线性方程，这种类型的近似失败。在一般尺度不变的情况下工作，并作为代表性的案例研究，我们制定和研究广义的HK方程的保守动力学，并重新考虑著名的系统，如保守和非保守的各向异性Kardar-Parisi-Zhang方程。通过结合使用动态重整化群分析和直接数值模拟，我们得出结论，SA的发生在二维表面需要动力学守恒。我们发现，此外，SA是不是通用的参数空间，而是需要，而具体的形状出现在运动的运动方程，其理由需要详细的信息，在每个特定的情况下被建模的动态过程中的条款。
英文摘要：
We expand a previous study [Phys. Rev. E 86, 051611 (2012)] on the conditions for occurrence of strong anisotropy (SA) in the scaling properties of two-dimensional surfaces displaying generic scale invariance. There, a natural Ansatz was proposed for SA, which arises naturally when analyzing data from e.g. thin-film production experiments. The Ansatz was tested in Gaussian (linear) models of surface dynamics and in non-linear models, like the Hwa-Kardar (HK) equation [Phys. Rev. Lett. 62, 1813 (1989)], which are susceptible of accurate approximations through the former. In contrast, here we analyze non-linear equations for which such type of approximations fail. Working within generically-scale-invariant situations, and as representative case studies, we formulate and study a generalization of the HK equation for conserved dynamics, and reconsider well-known systems, such as the conserved and the non-conserved anisotropic Kardar-Parisi-Zhang equations. Through the combined use of Dynamic Renormalization Group analysis and direct numerical simulations, we conclude that the occurrence of SA in two-dimensional surfaces requires dynamics to be conserved. We find that, moreover, SA is not generic in parameter space but requires, rather, specific shapes from the terms appearing in the equation of motion, whose justification needs detailed information on the dynamical process that is being modeled in each particular case.
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