守恒和非守恒KPZ方程标度奇异性的重整化群分析

Renormalization-Group Analysis of Anomalous Dynamic Scaling of the Conservative and Non-Conservative Kardar-Parisi-Zhang Equation

采用表面界面生长方程动力学标度奇异性的动力学重整化群理论,研究了守恒和非守恒Kardar-Parisi-Zhang(KPZ)方程的动力学标度奇异性.通过分析相应局域倾斜度的演化动力学方程的标度行为,得到了奇异标度指数κ和粗糙度指数的表达式.结果表明:生长方程的动力学标度性质与基底维数d无关,两个方程不具有奇异标度性质,均呈现Family-Vicsek正常标度关系,这和使用直接标度分析方法得到的结果一致.

A dynamic renormalization-group theory is applied to analyze the anomalously dynamic scaling property of the kinetic roughening growth equation of the conservative and nonconservative Kardar-Parisi-Zhang equations. The anomalous scaling exponent and roughness exponent were obtained by analyzing the scaling behavior of the corresponding time evolution equation for the local derivatives. The results show that the dynamic scaling property of a growth equation is independent of the dimension of the system. These two equations do not have the anomalous scaling property, but both exhibit Family-Vicsek scaling. Our results are consistent with previous calculations which make use of scaling analysis.