论文标题
界面增长中的高度分布：平均过程的作用
Height distributions in interface growth: The role of the averaging process
论文作者
论文摘要
To quantitatively characterize height distributions (HDs), one uses adimensional ratios of their first central moments ($m_n$) or cumulants ($κ_n$), especially the skewness $S$ and kurtosis $K$, whose accurate estimate demands an averaging over all $L^d$ points of the height profile at a given time, in translation-invariant interfaces, and over $N$ independent samples.一种方法是为每个样本计算$ m_n（t）$ [或$κ_n（t）$]，然后为$ n $接口进行平均值，其中仅计算出$ s $和$ k $。另一种方法是直接计算每个接口的比率，然后平均$ n $值。然而，事实证明，从这些“接口统计”中估算时，增长制度的$ s $和$ k $在以前的某些工作中已经观察到的，并通过对属于1D和2D siles siles siles $ l = const $ l = const。 Importantly, I demonstrate that with "1-point statistics'', i.e., by calculating $m_n(t)$ [or $κ_n(t)$] once for all $N L^d$ heights together, these corrections become very weak. However, I find that this "1-point'' approach fails in uncovering the universality of the HDs in the steady state regime (SSR) of systems whose average height, $ \ bar {h} $，是一个波动的变量。实际上，如下所示，在此制度中，1-PT的高度演变为$ h（t）= \ bar {h}（t） +s_λa^{1/2} l^αζζ + \ cdots $ - 其中$ p（ζ）$是基础的ssr hd-ssr hd- and $ sim sim sim sim sim $ \ bar} t^{ - 1/2} $和$ k_ {1pt} \ sim t^{ - 1} $。但是，通过分析$ p（h- \ bar {h}）$，可以准确确定$ p（ζ）$的累积物。
To quantitatively characterize height distributions (HDs), one uses adimensional ratios of their first central moments ($m_n$) or cumulants ($κ_n$), especially the skewness $S$ and kurtosis $K$, whose accurate estimate demands an averaging over all $L^d$ points of the height profile at a given time, in translation-invariant interfaces, and over $N$ independent samples. One way of doing this is by calculating $m_n(t)$ [or $κ_n(t)$] for each sample and then carrying out an average of them for the $N$ interfaces, with $S$ and $K$ being calculated only at the end. Another approach consists in directly calculating the ratios for each interface and, then, averaging the $N$ values. It turns out, however, that $S$ and $K$ for the growth regime HDs display strong finite-size and -time effects when estimated from these "interface statistics", as already observed in some previous works and clearly shown here, through extensive simulations of several discrete growth models belonging to the EW and KPZ classes on 1D and 2D substrates of sizes $L=const.$ and $L \sim t$. Importantly, I demonstrate that with "1-point statistics'', i.e., by calculating $m_n(t)$ [or $κ_n(t)$] once for all $N L^d$ heights together, these corrections become very weak. However, I find that this "1-point'' approach fails in uncovering the universality of the HDs in the steady state regime (SSR) of systems whose average height, $\bar{h}$, is a fluctuating variable. In fact, as demonstrated here, in this regime the 1-pt height evolves as $h(t) = \bar{h}(t) + s_λ A^{1/2} L^α ζ+ \cdots$ -- where $P(ζ)$ is the underlying SSR HD -- and the fluctuations in $\bar{h}$ yield $S_{1pt} \sim t^{-1/2}$ and $K_{1pt} \sim t^{-1}$. Nonetheless, by analyzing $P(h-\bar{h})$, the cumulants of $P(ζ)$ can be accurately determined.
