论文标题
具有远距离时间和空间相关性的Kardar-Parisi-Zhang生长中动力学粗糙的概率分布
Probability distributions for kinetic roughening in the Kardar-Parisi-Zhang growth with long-range temporal and spatial correlations
论文作者
论文摘要
我们以数值方式研究了基于平方界面宽度$ W^2（l，t）$和界面高度$ h（x，t）$在（1+1）-Dimemensional-paris-Parisi-parisi-Zhang（KPZ）增长系统中的远程时间和空间相关性的影响。通过大量的数值模拟，我们发现远距离相关的噪声不会显着影响界面宽度的分布形式。通常，当时间相关指数$θ\ ge 0 $时，$ w^2（l，t）$ obeys obeys obeys obeys obeys obeys obeys obeys obeys obeys obeys obeys obeys。另一方面，远距离相关的噪声的影响显然与时间相关的情况有所不同。我们的结果表明，当空间相关指数$ρ\ le 0.20 $时，$ w^2（l，t）$的分布形式接近对数正态分布，当$ρ> 0.20 $接近时，分布将变得更加不对称，陡峭，胖尾，并且趋于不知名的分布形式。相比之下，界面高度的概率分布在时间和空间相关的KPZ系统中也提供了，在整个相关性方案中彼此之间彼此之间的特征截然不同。对于时间相关，高度分布满足Tracy-Widom Gaussian正交集合（TW-GOE）时，当$θ\至0 $，并且随着$θ$的增加，高度分布持续到未知分布。但是，对于空间相关性，高度分布逐渐从TW-GOE分布过渡到标准高斯形式。
We investigate numerically the effects of long-range temporal and spatial correlations based on the rescaled distributions of the squared interface width $W^2(L,t)$ and the interface height $h(x,t)$ in the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) growth system within the early growth regimes. Through extensive numerical simulations, we find that long-range temporally correlated noise could not significantly impact the distribution form of the interface width. Generally, $W^2(L,t)$ obeys approximately lognormal distribution when the temporal correlation exponent $θ\ge 0$. On the other hand, the effects of long-range spatially correlated noise are evidently different from the temporally correlated case. Our results show that, when the spatial correlation exponent $ρ\le 0.20$, the distribution forms of $W^2(L,t)$ approach the lognormal distribution, and when $ρ> 0.20$, the distribution becomes more asymmetric, steep, and fat-tailed, and tends to an unknown distribution form. As a comparison, probability distributions of the interface height are also provided in the temporally and spatially correlated KPZ system, exhibiting quite different characteristics from each other within the whole correlated regimes. For the temporal correlation, the height distributions satisfy Tracy-Widom Gaussian orthogonal ensemble (TW-GOE) when $θ\to 0$, and with increasing $θ$, the height distributions crossover continously to an unknown distribution. However, for the spatial correlation, the height distributions gradually transition from the TW-GOE distribution to the standard Gaussian form.
