论文标题
$ 2+1 $尺寸的Kardar-Parisi-Zhang指数
The Kardar-Parisi-Zhang exponents for the $2+1$ dimensions
论文作者
论文摘要
Kardar-Parisi-Zhang（KPZ）方程已与从经典到量子物理学的物理，化学和生长现象的大量重要随机过程相关。该领域的中心追求是搜索越来越精确的普遍增长指数。值得注意的是，精确的增长指数仅以$ 1+1 $尺寸而闻名。在这项工作中，我们提出了将这些指数与粗糙界面的分形维直接关联的物理和几何分析方法。基于此，我们确定了$ 2+1 $尺寸的增长指数，这与薄膜实验和精确模拟的结果一致。我们还迈出了$ d+1 $尺寸的解决方案的第一步，我们的结果表明上临界维度的不存在。
The Kardar-Parisi-Zhang (KPZ) equation has been connected to a large number of important stochastic processes in physics, chemistry and growth phenomena, ranging from classical to quantum physics. The central quest in this field is the search for ever more precise universal growth exponents. Notably, exact growth exponents are only known for $1+1$ dimensions. In this work, we present physical and geometric analytical methods that directly associate these exponents to the fractal dimension of the rough interface. Based on this, we determine the growth exponents for the $2+1$ dimensions, which are in agreement with the results of thin films experiments and precise simulations. We also make a first step towards a solution in $d+1$ dimensions, where our results suggest the inexistence of an upper critical dimension.
