含时空关联噪声生长方程的标度奇异性分析

基于动力学重整化群理论研究表面界面生长动力学标度奇异性问题， 得到含时空关联噪声的表面生长方程标度奇异指数的一般结果，并将此方法应用于几种典型的局域生长方程——Kardar-Parisi-Zhang（KPZ）方程、线性生长方程、Lai-Das Sarma-Villain（LDV）方程.结果表明，在长波长极限下局域生长方程的动力学标度奇异性与最相关项、基底维数以及噪声有关，并且若出现标度奇异性，只会是超粗化（super rough）奇异标度行为，而不是内禀（intrinsically）奇异标度行为. 关键词： 标度奇异性 动力学重整化群理论 时空关联噪声

Anomalous scaling of the growth equations with spatially and temporally correlated noise

A dynamic renormalization-group method is generalized to explore the anomalously dynamic scaling property of kinetic roughening growth equation and the general conclusion on the anomalous exponents of the growth equation with spatially and temporally correlated noise is drawn. The results of the anomalous exponents are employed in several typical local growth equations，which include the Kardar-Parisi-Zhang（KPZ）equation，linear equation and Lai-Das Sarma-Villain（LDV） equation, to judge the condition of anomalous scaling behaviors. Analysis shows that within the long wavelength limit the dynamic scaling property of a growth equation is related to the most relevant term, the dimension of the system and noise; and if the anomalous scaling of the equation exists, super_roughening instead of intrinsic anomalous roughening will be displayed in local growth models.