Surface growth processes can be significantly affected by long-range temporal correlations. In this work, we perform extensive numerical simulations of a (1+1)- and (2+1)-dimensional ballistic deposition (BD) model driven by temporally correlated noise, which is regarded as the temporal correlated Kardar-Parisi-Zhang universality class. Our results are compared with the existing theoretical predictions and numerical simulations. When the temporal correlation exponent is above a certain threshold, BD surfaces develop gradually faceted patterns. We find that the temporal correlated BD system displays nontrivial dynamic properties, and the characteristic roughness exponents satisfy $\alpha \simeq {\alpha }_{\mathrm{loc}}<{\alpha }_s$ in (1+1) dimensions, which is beyond the existing dynamic scaling classifications.

中文翻译：

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具有时间相关噪声的表面生长的广泛数值模拟

表面生长过程可能会受到远程时间相关性的显着影响。在这项工作中，我们对由时间相关噪声驱动的（1 + 1）和（2 + 1）维弹道沉积（BD）模型进行广泛的数值模拟，这被认为是时间相关的Kardar-Parisi-Zhang普遍性类。我们的结果与现有的理论预测和数值模拟进行了比较。当时间相关指数高于某个阈值时，BD表面逐渐形成刻面图案。我们发现时间相关的BD系统显示出非平凡的动力学特性，并且特征粗糙度指数满足$\alpha \simeq {\alpha }_{\mathrm{位置}}<{\alpha }_s$ （1 + 1）维，这超出了现有的动态缩放分类。