arXiv 1711.096522017-11cond-mat.stat-mech

KPZ模型：高度梯度起伏和倾斜方法

KPZ models: height-gradient fluctuations and the tilt method

M. F. Torres, R. C. Buceta

备注：: 9 pages, 3 figures. We study in more detail the local fluctuations of the height gradient with the measurement window and modify the work and conclusions to reflect that

摘要：

当属于KPZ普适类的生长界面以平均斜率$m$倾斜时，其平均速度在$\fracΛ{2}\,m^2$中增加，其中$Λ$与KPZ方程的非线性系数$λ$有关。然而，这种关联成立的必要条件是，当界面倾斜时，均方高度梯度在$b\, m^2$中增加。对于连续的KPZ方程，得到了$b = 1$和关系式$Λ=λ$.在这项工作中，我们研究的高度梯度的局部波动，通过分析的$b$值。我们表明，对于1维离散KPZ模型，$b$与选择用于计算高度梯度的离散化步骤$s$具有幂律依赖性，并且随着$s$的增加，$b$变为$1$。其幂律指数$γ_b$与界面平均速度的有限尺寸修正相关的指数$\textit{i.e.}$ $γ_b=2(ζ-1)$相匹配，其中$ζ$是全局粗糙度指数。我们还展示了如何限制（无限制）的增长模型，$b$的值从下面（上面）$s$增加$1$。

英文摘要：

When a growing interface belonging to the KPZ universality class is tilted with average slope $m$, its average velocity increases in $\fracΛ{2}\,m^2$, where $Λ$ is related to the nonlinear coefficient $λ$ of the KPZ equation. Nevertheless, a necessary condition for this association to hold true is that the mean square height-gradient increases in $b\, m^2$ when the interface is tilted. For the continuous KPZ equation $b = 1$ and the relation $Λ=λ$ is achieved. In this work, we study the local fluctuations of the height gradient through an analysis of the values of $b$. We show that, for 1-dimensional discrete KPZ models, $b$ has a power-law dependence with the discretization step $s$ chosen to calculate the height gradient and $b$ goes to $1$ as $s$ increases. Its power-law exponent $γ_b$ matches the exponent associated with the finite-size corrections of the interface average velocity, $\textit{i.e.}$ $γ_b=2(ζ-1)$, where $ζ$ is the global roughness exponent. We also show how, for restricted (unrestricted) growth models, the value of $b$ goes to $1$ from below (above) as $s$ increases.

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英文摘要：

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